Balanced vs Unbalanced Forces
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Middle School Physical Science › Balanced vs Unbalanced Forces
A student compares two situations with the same book on the same table.
Situation 1: The book is resting. Forces on the book: weight $10,\text{N}$ downward and normal force $10,\text{N}$ upward.
Situation 2: The student pushes the book to the right with $12,\text{N}$ while friction pulls left with $7,\text{N}$ (the $10,\text{N}$ weight and $10,\text{N}$ normal force still act).
Which statement correctly compares the net force and motion in the two situations?
Situation 1 is balanced only if the book is moving; since it is at rest, the forces must be unbalanced.
Situation 2 is balanced because there are four forces acting, so the net force must be zero.
Situation 1 is unbalanced and the book accelerates upward; Situation 2 is balanced so it moves at constant speed.
Situation 1 is balanced with $F_{\text{net}}=0$ so there is no acceleration; Situation 2 is unbalanced with $F_{\text{net}}=5,\text{N}$ to the right so the book accelerates right.
Explanation
This question tests understanding of the critical difference between balanced forces (F_net = 0, no acceleration) and unbalanced forces (F_net ≠ 0, acceleration occurs). Balanced forces occur when all forces acting on an object sum to zero (F_net = 0)—this can happen with two equal magnitude opposite direction forces canceling out (like weight 10 N down and normal force 10 N up), or with multiple forces that completely cancel when added as vectors. When forces are balanced, Newton's First Law applies: an object at rest will stay at rest, and an object moving will continue at the same speed in the same direction (constant velocity), because with no net force, there's no acceleration (a = 0 when F_net = 0). Unbalanced forces occur when forces don't sum to zero (F_net ≠ 0), meaning one direction has more force than the opposite direction, and Newton's Second Law applies: the object accelerates (F_net = ma) in the direction of the net force—this changes the motion by speeding up, slowing down, or changing direction. Scenario 1 shows balanced forces (all forces cancel, F_net = 0) resulting in no acceleration (stays at rest), while Scenario 2 shows unbalanced forces (forces don't cancel, F_net = 5 N right) resulting in acceleration to the right (motion changes)—the key difference is the net force: zero net force means no motion change (Newton's First Law), nonzero net force means motion change via acceleration (Newton's Second Law). Choice B is correct because it properly identifies forces as balanced when they sum to zero, or unbalanced when they don't, and correctly predicts no acceleration for balanced forces (F_net = 0 → a = 0) while accurately predicting acceleration for unbalanced forces in direction of F_net. Choice A is incorrect because it incorrectly identifies balanced forces as unbalanced (or vice versa), possibly by ignoring directions when calculating net force, and predicts acceleration when forces are balanced (F_net = 0), violating Newton's First Law which states balanced forces produce no acceleration. To determine if forces are balanced or unbalanced: (1) identify all forces acting on the object (draw or list them with magnitudes and directions), (2) add forces as vectors considering directions (forces in same direction add, forces in opposite directions subtract), (3) calculate net force F_net (if all cancel → F_net = 0 balanced, if don't cancel → F_net = some value in some direction unbalanced), (4) predict motion: F_net = 0 means no acceleration (stays at rest or constant velocity), F_net ≠ 0 means acceleration = F_net/m in the net force direction. Common situations: book sitting still on table has balanced forces (definitely not accelerating, so F_net = 0), car cruising at steady speed on highway has balanced forces (constant velocity means a = 0 means F_net = 0 even though moving), car speeding up has unbalanced forces (accelerating means F_net ≠ 0 by Newton's Second Law), and falling object near start has unbalanced forces (weight > air resistance, F_net down, accelerates down) but at terminal velocity has balanced forces (weight = air resistance, F_net = 0, constant velocity downward)—the motion outcome (accelerating or not) tells you about force balance, and force balance tells you about motion outcome, they're connected through Newton's Laws.
A car is traveling straight on a level road.
Case 1: The engine provides $500,\text{N}$ forward while air resistance and friction total $500,\text{N}$ backward.
Case 2: The engine provides $700,\text{N}$ forward while air resistance and friction total $500,\text{N}$ backward.
How does the motion differ between Case 1 and Case 2?
Case 2 is balanced because there are more newtons forward, so the car’s speed stays the same.
Case 1 has $F_{\text{net}}=1000,\text{N}$ forward so the car accelerates; Case 2 has $F_{\text{net}}=0$ so it is at rest.
Both cases are balanced because the car is moving, so neither case can involve acceleration.
Case 1 has $F_{\text{net}}=0$ so the car can move at constant velocity; Case 2 has $F_{\text{net}}=200,\text{N}$ forward so the car accelerates forward.
Explanation
This question tests understanding of the critical difference between balanced forces (F_net = 0, no acceleration) and unbalanced forces (F_net ≠ 0, acceleration occurs). Balanced forces occur when all forces acting on an object sum to zero (F_net = 0)—this can happen with two equal magnitude opposite direction forces canceling out (like weight 10 N down and normal force 10 N up), or with multiple forces that completely cancel when added as vectors. When forces are balanced, Newton's First Law applies: an object at rest will stay at rest, and an object moving will continue at the same speed in the same direction (constant velocity), because with no net force, there's no acceleration (a = 0 when F_net = 0). Unbalanced forces occur when forces don't sum to zero (F_net ≠ 0), meaning one direction has more force than the opposite direction, and Newton's Second Law applies: the object accelerates (F_net = ma) in the direction of the net force—this changes the motion by speeding up, slowing down, or changing direction. Scenario Case 1 shows balanced forces (all forces cancel, F_net = 0) resulting in constant velocity motion (no acceleration), while Scenario Case 2 shows unbalanced forces (forces don't cancel, F_net = 200 N forward) resulting in acceleration forward (motion changes)—the key difference is the net force: zero net force means no motion change (Newton's First Law), nonzero net force means motion change via acceleration (Newton's Second Law). Choice A is correct because it properly identifies forces as balanced when they sum to zero, or unbalanced when they don't, and correctly predicts no acceleration for balanced forces (F_net = 0 → a = 0) while accurately predicting acceleration for unbalanced forces in direction of F_net. Choice B incorrectly identifies balanced forces as unbalanced (or vice versa), possibly by ignoring directions when calculating net force, makes calculation error: adds forces without considering opposite directions (500 N forward + 500 N backward = 1000 N instead of 0), and predicts constant velocity when forces are unbalanced (F_net ≠ 0), violating Newton's Second Law which requires acceleration when net force exists. To determine if forces are balanced or unbalanced: (1) identify all forces acting on the object (draw or list them with magnitudes and directions), (2) add forces as vectors considering directions (forces in same direction add, forces in opposite directions subtract), (3) calculate net force F_net (if all cancel → F_net = 0 balanced, if don't cancel → F_net = some value in some direction unbalanced), (4) predict motion: F_net = 0 means no acceleration (stays at rest or constant velocity), F_net ≠ 0 means acceleration = F_net/m in the net force direction. Common situations: book sitting still on table has balanced forces (definitely not accelerating, so F_net = 0), car cruising at steady speed on highway has balanced forces (constant velocity means a = 0 means F_net = 0 even though moving), car speeding up has unbalanced forces (accelerating means F_net ≠ 0 by Newton's Second Law), and falling object near start has unbalanced forces (weight > air resistance, F_net down, accelerates down) but at terminal velocity has balanced forces (weight = air resistance, F_net = 0, constant velocity downward)—the motion outcome (accelerating or not) tells you about force balance, and force balance tells you about motion outcome, they're connected through Newton's Laws.
A cart rolls to the right at a constant speed. The student measures the forward push on the cart as 6 N to the right and the friction force as 6 N to the left. Which statement is correct?
Forces are balanced, so the cart must be at rest.
Forces are unbalanced ($F_{net}=12\text{ N}$ right), so the cart must be speeding up.
Forces are balanced ($F_{net}=0$), so the cart has no acceleration and keeps a constant velocity.
Forces are unbalanced because the cart is moving, so it must be accelerating.
Explanation
This question tests understanding of the critical difference between balanced forces (F_net = 0, no acceleration) and unbalanced forces (F_net ≠ 0, acceleration occurs). Balanced forces occur when all forces acting on an object sum to zero (F_net = 0)—this can happen with two equal magnitude opposite direction forces canceling out (like weight 10 N down and normal force 10 N up), or with multiple forces that completely cancel when added as vectors. When forces are balanced, Newton's First Law applies: an object at rest will stay at rest, and an object moving will continue at the same speed in the same direction (constant velocity), because with no net force, there's no acceleration (a = 0 when F_net = 0). Unbalanced forces occur when forces don't sum to zero (F_net ≠ 0), meaning one direction has more force than the opposite direction, and Newton's Second Law applies: the object accelerates (F_net = ma) in the direction of the net force—this changes the motion by speeding up, slowing down, or changing direction. In this situation, the forces are balanced because the rightward push (6 N) equals the leftward friction (6 N), giving F_net = 0. With net force of zero, Newton's First Law predicts the object will continue moving at constant velocity if currently moving—there will be no acceleration because acceleration requires net force (F = ma), and with F_net = 0, we must have a = 0. Choice A is correct because it properly identifies forces as balanced when they sum to zero, and correctly predicts no acceleration for balanced forces (F_net = 0 → a = 0). Choice C incorrectly identifies balanced forces as unbalanced, possibly by ignoring that motion at constant velocity can occur with balanced forces, and predicts acceleration when forces are balanced (F_net = 0), violating Newton's First Law which states balanced forces produce no acceleration. To determine if forces are balanced or unbalanced: (1) identify all forces acting on the object (draw or list them with magnitudes and directions), (2) add forces as vectors considering directions (forces in same direction add, forces in opposite directions subtract), (3) calculate net force F_net (if all cancel → F_net = 0 balanced, if don't cancel → F_net = some value in some direction unbalanced), (4) predict motion: F_net = 0 means no acceleration (stays at rest or constant velocity), F_net ≠ 0 means acceleration = F_net/m in the net force direction. Common situations: book sitting still on table has balanced forces (definitely not accelerating, so F_net = 0), car cruising at steady speed on highway has balanced forces (constant velocity means a = 0 means F_net = 0 even though moving), car speeding up has unbalanced forces (accelerating means F_net ≠ 0 by Newton's Second Law), and falling object near start has unbalanced forces (weight > air resistance, F_net down, accelerates down) but at terminal velocity has balanced forces (weight = air resistance, F_net = 0, constant velocity downward)—the motion outcome (accelerating or not) tells you about force balance, and force balance tells you about motion outcome, they're connected through Newton's Laws.
A cart is moving to the right at a constant speed in a straight line. A fan pushes the cart forward with 4 N to the right, and friction is 4 N to the left. Which statement is correct?
The forces are balanced ($F_{net}=0$), so the cart has no acceleration and keeps a constant velocity.
The forces are unbalanced ($F_{net}=8\text{ N}$ right), so the cart speeds up.
The forces are unbalanced because the cart is moving; moving objects always have unbalanced forces.
The forces are balanced, so the cart must slow down and stop.
Explanation
This question tests understanding of the critical difference between balanced forces (F_net = 0, no acceleration) and unbalanced forces (F_net ≠ 0, acceleration occurs). Balanced forces occur when all forces acting on an object sum to zero (F_net = 0)—this can happen with two equal magnitude opposite direction forces canceling out (like weight 10 N down and normal force 10 N up), or with multiple forces that completely cancel when added as vectors. When forces are balanced, Newton's First Law applies: an object at rest will stay at rest, and an object moving will continue at the same speed in the same direction (constant velocity), because with no net force, there's no acceleration (a = 0 when F_net = 0). Unbalanced forces occur when forces don't sum to zero (F_net ≠ 0), meaning one direction has more force than the opposite direction, and Newton's Second Law applies: the object accelerates (F_net = ma) in the direction of the net force—this changes the motion by speeding up, slowing down, or changing direction. The forces are balanced because the rightward fan force (4 N) equals the leftward friction (4 N), giving F_net = 4 N right - 4 N left = 0. With net force of zero, Newton's First Law predicts the object will continue moving at constant velocity if currently moving—there will be no acceleration because acceleration requires net force (F = ma), and with F_net = 0, we must have a = 0. Choice A is correct because it properly identifies forces as balanced when they sum to zero, and correctly predicts no acceleration for balanced forces (F_net = 0 → a = 0). Choice D incorrectly identifies balanced forces as unbalanced (or vice versa), possibly by ignoring directions when calculating net force and claims only objects at rest can have balanced forces, when actually constant velocity also has F_net = 0 (balanced). To determine if forces are balanced or unbalanced: (1) identify all forces acting on the object (draw or list them with magnitudes and directions), (2) add forces as vectors considering directions (forces in same direction add, forces in opposite directions subtract), (3) calculate net force F_net (if all cancel → F_net = 0 balanced, if don't cancel → F_net = some value in some direction unbalanced), (4) predict motion: F_net = 0 means no acceleration (stays at rest or constant velocity), F_net ≠ 0 means acceleration = F_net/m in the net force direction. Common situations: book sitting still on table has balanced forces (definitely not accelerating, so F_net = 0), car cruising at steady speed on highway has balanced forces (constant velocity means a = 0 means F_net = 0 even though moving), car speeding up has unbalanced forces (accelerating means F_net ≠ 0 by Newton's Second Law), and falling object near start has unbalanced forces (weight > air resistance, F_net down, accelerates down) but at terminal velocity has balanced forces (weight = air resistance, F_net = 0, constant velocity downward)—the motion outcome (accelerating or not) tells you about force balance, and force balance tells you about motion outcome, they're connected through Newton's Laws.
A skydiver has just jumped from a plane. At that moment, the forces are: weight $800,\text{N}$ downward and air resistance $100,\text{N}$ upward.
Which statement best describes the force balance and the motion?
Forces are unbalanced with $F_{\text{net}}=700,\text{N}$ downward, so the skydiver accelerates downward.
Forces are unbalanced with $F_{\text{net}}=900,\text{N}$ downward, so the skydiver accelerates downward.
Forces are balanced ($F_{\text{net}}=0$), so the skydiver falls at constant speed.
Forces are balanced because there are two forces, so the skydiver does not move.
Explanation
This question tests understanding of the critical difference between balanced forces (F_net = 0, no acceleration) and unbalanced forces (F_net ≠ 0, acceleration occurs). Balanced forces occur when all forces acting on an object sum to zero (F_net = 0)—this can happen with two equal magnitude opposite direction forces canceling out (like weight 10 N down and normal force 10 N up), or with multiple forces that completely cancel when added as vectors. When forces are balanced, Newton's First Law applies: an object at rest will stay at rest, and an object moving will continue at the same speed in the same direction (constant velocity), because with no net force, there's no acceleration (a = 0 when F_net = 0). Unbalanced forces occur when forces don't sum to zero (F_net ≠ 0), meaning one direction has more force than the opposite direction, and Newton's Second Law applies: the object accelerates (F_net = ma) in the direction of the net force—this changes the motion by speeding up, slowing down, or changing direction. The forces are unbalanced because the downward weight (800 N) exceeds the upward air resistance (100 N), giving F_net = 800 - 100 = 700 N downward; this net force (F_net ≠ 0) will cause acceleration by Newton's Second Law: F_net = ma, so the object will accelerate in the direction of the net force downward, changing its motion by speeding up downward. Choice B is correct because it properly identifies forces as unbalanced when they don't sum to zero, accurately predicts acceleration for unbalanced forces in direction of F_net, and properly calculates net force by considering force directions and magnitudes. Choice A incorrectly identifies unbalanced forces as balanced, possibly by ignoring directions when calculating net force, and predicts constant velocity when forces are unbalanced (F_net ≠ 0), violating Newton's Second Law which requires acceleration when net force exists. To determine if forces are balanced or unbalanced: (1) identify all forces acting on the object (draw or list them with magnitudes and directions), (2) add forces as vectors considering directions (forces in same direction add, forces in opposite directions subtract), (3) calculate net force F_net (if all cancel → F_net = 0 balanced, if don't cancel → F_net = some value in some direction unbalanced), (4) predict motion: F_net = 0 means no acceleration (stays at rest or constant velocity), F_net ≠ 0 means acceleration = F_net/m in the net force direction. Common situations: book sitting still on table has balanced forces (definitely not accelerating, so F_net = 0), car cruising at steady speed on highway has balanced forces (constant velocity means a = 0 means F_net = 0 even though moving), car speeding up has unbalanced forces (accelerating means F_net ≠ 0 by Newton's Second Law), and falling object near start has unbalanced forces (weight > air resistance, F_net down, accelerates down) but at terminal velocity has balanced forces (weight = air resistance, F_net = 0, constant velocity downward)—the motion outcome (accelerating or not) tells you about force balance, and force balance tells you about motion outcome, they're connected through Newton's Laws.
A book is resting on a table. The book’s weight is 10 N downward, and the table pushes up on the book with a normal force of 10 N upward. Which statement best describes the forces and the book’s motion?
Forces are unbalanced ($F_{net}=20\text{ N}$ upward), so the book accelerates upward.
Forces are balanced ($F_{net}=0$), so the book has no acceleration and stays at rest.
Forces are balanced ($F_{net}=0$), so the book must be moving at constant speed across the table.
Forces are unbalanced because there are two forces, so the book accelerates downward.
Explanation
This question tests understanding of the critical difference between balanced forces (F_net = 0, no acceleration) and unbalanced forces (F_net ≠ 0, acceleration occurs). Balanced forces occur when all forces acting on an object sum to zero (F_net = 0)—this can happen with two equal magnitude opposite direction forces canceling out (like weight 10 N down and normal force 10 N up), or with multiple forces that completely cancel when added as vectors. When forces are balanced, Newton's First Law applies: an object at rest will stay at rest, and an object moving will continue at the same speed in the same direction (constant velocity), because with no net force, there's no acceleration (a = 0 when F_net = 0). Unbalanced forces occur when forces don't sum to zero (F_net ≠ 0), meaning one direction has more force than the opposite direction, and Newton's Second Law applies: the object accelerates (F_net = ma) in the direction of the net force—this changes the motion by speeding up, slowing down, or changing direction. In this situation, the forces are balanced because the upward normal force (10 N) equals the downward weight (10 N), giving F_net = 10 N up + 10 N down = 0. With net force of zero, Newton's First Law predicts the object will remain at rest if currently stationary—there will be no acceleration because acceleration requires net force (F = ma), and with F_net = 0, we must have a = 0. Choice B is correct because it properly identifies forces as balanced when they sum to zero, and correctly predicts no acceleration for balanced forces (F_net = 0 → a = 0). Choice C incorrectly predicts constant velocity motion when the book is described as resting, violating the scenario where it's at rest with balanced forces. To determine if forces are balanced or unbalanced: (1) identify all forces acting on the object (draw or list them with magnitudes and directions), (2) add forces as vectors considering directions (forces in same direction add, forces in opposite directions subtract), (3) calculate net force F_net (if all cancel → F_net = 0 balanced, if don't cancel → F_net = some value in some direction unbalanced), (4) predict motion: F_net = 0 means no acceleration (stays at rest or constant velocity), F_net ≠ 0 means acceleration = F_net/m in the net force direction. Common situations: book sitting still on table has balanced forces (definitely not accelerating, so F_net = 0), car cruising at steady speed on highway has balanced forces (constant velocity means a = 0 means F_net = 0 even though moving), car speeding up has unbalanced forces (accelerating means F_net ≠ 0 by Newton's Second Law), and falling object near start has unbalanced forces (weight > air resistance, F_net down, accelerates down) but at terminal velocity has balanced forces (weight = air resistance, F_net = 0, constant velocity downward)—the motion outcome (accelerating or not) tells you about force balance, and force balance tells you about motion outcome, they're connected through Newton's Laws.
A cart is pushed to the right with 10 N while friction is 10 N to the left. The cart is already moving to the right. What will happen to the cart’s motion?
It slows down because friction always makes objects stop, even if forces balance.
It speeds up because a force is applied to the right.
It continues at constant velocity because $F_{net}=0$ (balanced forces).
It accelerates to the left because friction is present.
Explanation
This question tests understanding of the critical difference between balanced forces (F_net = 0, no acceleration) and unbalanced forces (F_net ≠ 0, acceleration occurs). Balanced forces occur when all forces acting on an object sum to zero (F_net = 0)—this can happen with two equal magnitude opposite direction forces canceling out (like weight 10 N down and normal force 10 N up), or with multiple forces that completely cancel when added as vectors. When forces are balanced, Newton's First Law applies: an object at rest will stay at rest, and an object moving will continue at the same speed in the same direction (constant velocity), because with no net force, there's no acceleration (a = 0 when F_net = 0). Unbalanced forces occur when forces don't sum to zero (F_net ≠ 0), meaning one direction has more force than the opposite direction, and Newton's Second Law applies: the object accelerates (F_net = ma) in the direction of the net force—this changes the motion by speeding up, slowing down, or changing direction. The forces are balanced because the rightward push (10 N) equals the leftward friction (10 N), giving F_net = 10 N right - 10 N left = 0. With net force of zero, Newton's First Law predicts the object will continue moving at constant velocity if currently moving—there will be no acceleration because acceleration requires net force (F = ma), and with F_net = 0, we must have a = 0. Choice C is correct because it properly identifies forces as balanced when they sum to zero, and correctly predicts no acceleration for balanced forces (F_net = 0 → a = 0). Choice B incorrectly identifies balanced forces as unbalanced (or vice versa), possibly by ignoring directions when calculating net force and predicts acceleration when forces are balanced (F_net = 0), violating Newton's First Law which states balanced forces produce no acceleration. To determine if forces are balanced or unbalanced: (1) identify all forces acting on the object (draw or list them with magnitudes and directions), (2) add forces as vectors considering directions (forces in same direction add, forces in opposite directions subtract), (3) calculate net force F_net (if all cancel → F_net = 0 balanced, if don't cancel → F_net = some value in some direction unbalanced), (4) predict motion: F_net = 0 means no acceleration (stays at rest or constant velocity), F_net ≠ 0 means acceleration = F_net/m in the net force direction. Common situations: book sitting still on table has balanced forces (definitely not accelerating, so F_net = 0), car cruising at steady speed on highway has balanced forces (constant velocity means a = 0 means F_net = 0 even though moving), car speeding up has unbalanced forces (accelerating means F_net ≠ 0 by Newton's Second Law), and falling object near start has unbalanced forces (weight > air resistance, F_net down, accelerates down) but at terminal velocity has balanced forces (weight = air resistance, F_net = 0, constant velocity downward)—the motion outcome (accelerating or not) tells you about force balance, and force balance tells you about motion outcome, they're connected through Newton's Laws.
A student wants to compare balanced and unbalanced forces using the same book on the same table. Which investigation plan best compares the motion outcomes?
Only measure the book’s weight in newtons; if weight is large, forces are unbalanced.
Push the book lightly and then push it lightly again; since the forces are the same, one trial will be balanced and one unbalanced.
Leave the book at rest (no push) and then push it so the push is greater than friction; observe that the first case has no acceleration and the second case speeds up.
Use two different books with different masses and push both; compare which one is heavier.
Explanation
This question tests understanding of the critical difference between balanced forces (F_net = 0, no acceleration) and unbalanced forces (F_net ≠ 0, acceleration occurs). Balanced forces occur when all forces acting on an object sum to zero (F_net = 0)—this can happen with two equal magnitude opposite direction forces canceling out (like weight 10 N down and normal force 10 N up), or with multiple forces that completely cancel when added as vectors. When forces are balanced, Newton's First Law applies: an object at rest will stay at rest, and an object moving will continue at the same speed in the same direction (constant velocity), because with no net force, there's no acceleration (a = 0 when F_net = 0). Unbalanced forces occur when forces don't sum to zero (F_net ≠ 0), meaning one direction has more force than the opposite direction, and Newton's Second Law applies: the object accelerates (F_net = ma) in the direction of the net force—this changes the motion by speeding up, slowing down, or changing direction. Scenario A shows balanced forces (all forces cancel, F_net = 0) resulting in no acceleration (stays at rest), while Scenario B shows unbalanced forces (forces don't cancel, F_net > 0 right) resulting in acceleration to the right (motion changes)—the key difference is the net force: zero net force means no motion change (Newton's First Law), nonzero net force means motion change via acceleration (Newton's Second Law). Choice B is correct because it properly identifies forces as balanced when they sum to zero, or unbalanced when they don't, and correctly predicts no acceleration for balanced forces (F_net = 0 → a = 0) while accurately predicting acceleration for unbalanced forces in direction of F_net. Choice A incorrectly identifies balanced forces as unbalanced (or vice versa), possibly by ignoring directions when calculating net force and confuses equal number of forces with balanced forces: two forces can be unbalanced if magnitudes differ (5 N right + 3 N left = 2 N net right). To determine if forces are balanced or unbalanced: (1) identify all forces acting on the object (draw or list them with magnitudes and directions), (2) add forces as vectors considering directions (forces in same direction add, forces in opposite directions subtract), (3) calculate net force F_net (if all cancel → F_net = 0 balanced, if don't cancel → F_net = some value in some direction unbalanced), (4) predict motion: F_net = 0 means no acceleration (stays at rest or constant velocity), F_net ≠ 0 means acceleration = F_net/m in the net force direction. Common situations: book sitting still on table has balanced forces (definitely not accelerating, so F_net = 0), car cruising at steady speed on highway has balanced forces (constant velocity means a = 0 means F_net = 0 even though moving), car speeding up has unbalanced forces (accelerating means F_net ≠ 0 by Newton's Second Law), and falling object near start has unbalanced forces (weight > air resistance, F_net down, accelerates down) but at terminal velocity has balanced forces (weight = air resistance, F_net = 0, constant velocity downward)—the motion outcome (accelerating or not) tells you about force balance, and force balance tells you about motion outcome, they're connected through Newton's Laws.
A box on the floor is pulled to the right with 14 N. Friction on the box is 9 N to the left. Which choice correctly describes whether the forces are balanced and what happens to the box?
Balanced; $F_{net}=0$, so the box stays at rest.
Unbalanced; $F_{net}=5\text{ N}$ to the left, so the box accelerates to the left.
Balanced; $F_{net}=23\text{ N}$ to the right, so the box moves at constant speed.
Unbalanced; $F_{net}=5\text{ N}$ to the right, so the box accelerates to the right.
Explanation
This question tests understanding of the critical difference between balanced forces (F_net = 0, no acceleration) and unbalanced forces (F_net ≠ 0, acceleration occurs). Balanced forces occur when all forces acting on an object sum to zero (F_net = 0)—this can happen with two equal magnitude opposite direction forces canceling out (like weight 10 N down and normal force 10 N up), or with multiple forces that completely cancel when added as vectors. When forces are balanced, Newton's First Law applies: an object at rest will stay at rest, and an object moving will continue at the same speed in the same direction (constant velocity), because with no net force, there's no acceleration (a = 0 when F_net = 0). Unbalanced forces occur when forces don't sum to zero (F_net ≠ 0), meaning one direction has more force than the opposite direction, and Newton's Second Law applies: the object accelerates (F_net = ma) in the direction of the net force—this changes the motion by speeding up, slowing down, or changing direction. The forces are unbalanced because the rightward pull (14 N) is greater than the leftward friction (9 N), giving net force F_net = 14 N - 9 N = 5 N to the right. This net force (F_net ≠ 0) will cause acceleration by Newton's Second Law: F_net = ma, so the object will accelerate in the direction of the net force to the right. Choice B is correct because it properly identifies forces as unbalanced when they don't sum to zero, accurately predicts acceleration for unbalanced forces in direction of F_net, and properly calculates net force by considering force directions and magnitudes. Choice C incorrectly identifies unbalanced forces as balanced (or vice versa), possibly by ignoring directions when calculating net force and makes calculation error: adds forces without considering opposite directions (14 N right + 9 N left = 23 N instead of 5 N). To determine if forces are balanced or unbalanced: (1) identify all forces acting on the object (draw or list them with magnitudes and directions), (2) add forces as vectors considering directions (forces in same direction add, forces in opposite directions subtract), (3) calculate net force F_net (if all cancel → F_net = 0 balanced, if don't cancel → F_net = some value in some direction unbalanced), (4) predict motion: F_net = 0 means no acceleration (stays at rest or constant velocity), F_net ≠ 0 means acceleration = F_net/m in the net force direction. Common situations: book sitting still on table has balanced forces (definitely not accelerating, so F_net = 0), car cruising at steady speed on highway has balanced forces (constant velocity means a = 0 means F_net = 0 even though moving), car speeding up has unbalanced forces (accelerating means F_net ≠ 0 by Newton's Second Law), and falling object near start has unbalanced forces (weight > air resistance, F_net down, accelerates down) but at terminal velocity has balanced forces (weight = air resistance, F_net = 0, constant velocity downward)—the motion outcome (accelerating or not) tells you about force balance, and force balance tells you about motion outcome, they're connected through Newton's Laws.
A skydiver has just jumped from a plane. At first, the weight downward is larger than the air resistance upward. What does this tell you about the net force and the skydiver’s motion?
Forces are balanced because gravity is always present, so there is no acceleration.
Forces are unbalanced ($F_{net}$ downward), so the skydiver accelerates downward (speeds up).
Forces are balanced ($F_{net}=0$), so the skydiver falls at constant speed.
Forces are unbalanced ($F_{net}$ upward), so the skydiver accelerates upward.
Explanation
This question tests understanding of the critical difference between balanced forces (F_net = 0, no acceleration) and unbalanced forces (F_net ≠ 0, acceleration occurs). Balanced forces occur when all forces acting on an object sum to zero (F_net = 0)—this can happen with two equal magnitude opposite direction forces canceling out (like weight 10 N down and normal force 10 N up), or with multiple forces that completely cancel when added as vectors. When forces are balanced, Newton's First Law applies: an object at rest will stay at rest, and an object moving will continue at the same speed in the same direction (constant velocity), because with no net force, there's no acceleration (a = 0 when F_net = 0). Unbalanced forces occur when forces don't sum to zero (F_net ≠ 0), meaning one direction has more force than the opposite direction, and Newton's Second Law applies: the object accelerates (F_net = ma) in the direction of the net force—this changes the motion by speeding up, slowing down, or changing direction. The forces are unbalanced because the downward weight exceeds the upward air resistance, giving F_net downward. This net force (F_net ≠ 0) will cause acceleration by Newton's Second Law: F_net = ma, so the object will accelerate in the direction of the net force downward, changing its motion by speeding up downward. Choice B is correct because it properly identifies forces as unbalanced when they don't sum to zero, and accurately predicts acceleration for unbalanced forces in direction of F_net. Choice A incorrectly identifies unbalanced forces as balanced, possibly by ignoring magnitudes when calculating net force, and predicts constant velocity when forces are unbalanced (F_net ≠ 0), violating Newton's Second Law which requires acceleration when net force exists. To determine if forces are balanced or unbalanced: (1) identify all forces acting on the object (draw or list them with magnitudes and directions), (2) add forces as vectors considering directions (forces in same direction add, forces in opposite directions subtract), (3) calculate net force F_net (if all cancel → F_net = 0 balanced, if don't cancel → F_net = some value in some direction unbalanced), (4) predict motion: F_net = 0 means no acceleration (stays at rest or constant velocity), F_net ≠ 0 means acceleration = F_net/m in the net force direction. Common situations: book sitting still on table has balanced forces (definitely not accelerating, so F_net = 0), car cruising at steady speed on highway has balanced forces (constant velocity means a = 0 means F_net = 0 even though moving), car speeding up has unbalanced forces (accelerating means F_net ≠ 0 by Newton's Second Law), and falling object near start has unbalanced forces (weight > air resistance, F_net down, accelerates down) but at terminal velocity has balanced forces (weight = air resistance, F_net = 0, constant velocity downward)—the motion outcome (accelerating or not) tells you about force balance, and force balance tells you about motion outcome, they're connected through Newton's Laws.