Forces and Free-Body Diagrams - AP Physics 1

1. A student pulls a sled on level snow with a rope angled $30^\circ$ above the horizontal. The sled accelerates to the right. Friction is present and air resistance is negligible. Which direction should the friction force on the sled point in the free-body diagram?
   Answer: To the left, opposite the sled's motion This question evaluates the understanding of force directions in free-body diagrams, particularly for friction in accelerating systems. Choose the sled as the system and consider all external forces from its surroundings. The friction force, being kinetic, acts opposite to the direction of the sled's velocity relative to the snow, which is to the right, so friction points to the left. Other forces include weight downward, normal upward, and tension along the rope at 30 degrees, with the horizontal component causing acceleration to the right despite friction. Choice A is incorrect because friction does not point in the direction of acceleration; it always opposes relative motion, not acceleration. When analyzing force directions, remember to determine friction's orientation based on the relative velocity between surfaces, then verify net force direction matches the observed acceleration.
2. A $0.80\,\text{kg}$ block is pressed against the ceiling by an upward applied force and remains at rest. Friction is negligible. Which forces act on the block? Select the correct free-body diagram.
   Answer: Forces: applied force upward, weight $mg$ downward, normal force from ceiling downward. This problem requires identifying forces in a free-body diagram for a block pressed against a ceiling at rest. When drawing a free-body diagram, we select the block as our object and include only forces acting directly on it. The forces are: weight (mg) acting downward from gravity, applied force acting upward from the push, and normal force acting downward from the ceiling (the ceiling pushes down on the block). Choice C incorrectly shows the normal force from the ceiling as upward, but the ceiling is above the block and pushes down on it—normal forces always push away from surfaces. Since the block is at rest, forces balance: the upward applied force equals the sum of weight and normal force, both downward. The essential strategy is to recognize that normal forces always push outward from surfaces, and when an object is pressed against a surface, that surface pushes back on the object.
3. A $0.50\,\text{kg}$ cart on a horizontal track is pushed to the right and speeds up. Friction is negligible. Which forces act on the cart? Select the correct free-body diagram.
   Answer: Forces: $mg$ downward, normal force upward, applied force to the right. This problem requires identifying forces in a free-body diagram for a cart that speeds up when pushed. When constructing a free-body diagram, we select the cart as our system and include only forces acting directly on it. The forces present are: weight (mg) acting downward from Earth's gravitational pull, normal force acting upward from the track supporting the cart, and the applied force acting horizontally to the right from the push. Choice C incorrectly adds a 'force of acceleration' to the right, but acceleration is not a force—it's the effect of unbalanced forces. Since friction is negligible and the cart accelerates to the right, the applied force is the only horizontal force, creating a net force rightward. The essential strategy is to identify only real forces from physical interactions and remember that acceleration results from net force, not from an additional 'acceleration force.'
4. A $4.0\,\text{kg}$ box is pushed against a vertical wall and remains at rest. Static friction is present between box and wall. Which forces act on the box? Select the correct free-body diagram.
   Answer: Forces: weight $mg$ downward, normal force from wall horizontal, applied push into wall horizontal, static friction upward. This problem requires identifying forces in a free-body diagram for a box pressed against a wall at rest. When creating a free-body diagram, we select the box as our object and include only forces acting directly on it. The forces are: weight (mg) acting downward from gravity, normal force acting horizontally outward from the wall (perpendicular to the wall surface), applied force acting horizontally into the wall from the push, and static friction acting upward along the wall to prevent the box from sliding down. Choice D incorrectly includes a 'force of rest' upward, but being at rest is not a force—it's a state resulting from balanced forces. Since the box doesn't move, vertical forces balance (friction up equals weight down) and horizontal forces balance (normal force equals applied force). The key strategy is to identify all contact forces at each surface and remember that static friction acts to prevent motion, not because of motion.
5. A 5.0 kg box sits at rest on a horizontal floor. A student pushes it horizontally to the right with 8.0 N, but it does not move. Static friction is present. Which forces act on the box? Stem: Which free-body diagram correctly represents the forces on the box?
   Answer: Forces: $mg$ downward; normal force upward; applied push 8.0 N right; static friction left. This question assesses the skill of identifying forces and constructing free-body diagrams in AP Physics 1. Choose the box as the system and identify all external forces acting on it. The forces include the gravitational force mg downward from Earth, the normal force upward from the floor, the applied push of 8.0 N to the right from the student, and static friction to the left from the floor opposing the push and preventing motion. Since the box remains at rest, static friction equals the push in magnitude but opposite in direction, maintaining equilibrium. Choice D is incorrect because it includes a force left exerted by the box on the student, but free-body diagrams only show forces on the system, not forces exerted by the system on other objects, per Newton's third law. To avoid errors, focus solely on forces acting on the chosen object and use Newton's laws to infer magnitudes when needed.
6. A student slides a $1.2\,\text{kg}$ book to the right across a table; it slows down after release. Kinetic friction is present. Which forces act on the book? Select the correct free-body diagram.
   Answer: Forces: $mg$ downward, normal force upward, kinetic friction to the left. This problem requires identifying forces in a free-body diagram for a sliding book that slows down. When creating a free-body diagram, we choose the book as our object and include only forces that act directly on it. The forces are: weight (mg) acting downward due to Earth's gravity, normal force acting upward from the table supporting the book, and kinetic friction acting opposite to the direction of motion (to the left, since the book slides right). Choice D incorrectly includes a 'force of motion' to the right, but motion itself is not a force—forces cause changes in motion. Since the book slows down while moving right, there must be a net force to the left, which is provided by friction alone. The key strategy is to identify only real forces from physical contacts or fields, and remember that friction always opposes the direction of sliding motion.
7. A block is on a horizontal surface and is pulled by a rope horizontally to the right. Friction is negligible. The block accelerates to the right. Which free-body diagram description is correct?
   Answer: Forces: weight down, normal up, tension right This question evaluates constructing free-body diagrams for accelerating objects with tension and negligible friction. Choose the block as the system and include forces from its environment. The real forces are weight downward, normal force upward from the surface, and tension to the right from the rope. With negligible friction and acceleration to the right, tension provides the net horizontal force. Choice D is incorrect because it includes a 'force of motion,' which is not a real force but a misconception. Always base free-body diagrams on actual physical interactions, and for acceleration, ensure net force direction matches the acceleration vector per Newton's second law.
8. Two students pull on opposite ends of a rope tied to a 4.0 kg box on a frictionless floor. Student 1 pulls right with 12 N; Student 2 pulls left with 5.0 N. The box accelerates right. Which forces act on the box? Stem: Which set of forces correctly represents the free-body diagram of the box?
   Answer: Forces: $mg$ downward; normal force upward; 12 N right; 5.0 N left. This question assesses the skill of identifying forces and constructing free-body diagrams in AP Physics 1. Select the box as the system and identify forces from external agents. The forces acting are the gravitational force mg downward from Earth, the normal force upward from the floor, the 12 N pull to the right from Student 1, and the 5.0 N pull to the left from Student 2. The acceleration to the right results from the net horizontal force of 7 N right, with no friction mentioned. Choice C is incorrect because it omits the 5.0 N left and adds an extra force right due to acceleration, but acceleration is the outcome of unbalanced real forces, not a separate force itself. For multiple applied forces, represent each as a distinct vector in the free-body diagram and calculate net force separately for verification.
9. A 2.0 kg book rests on a horizontal table. Friction is negligible. The book is pulled to the right by a horizontal string with tension 6.0 N, and it accelerates to the right. Which set of forces acts on the book? Stem: Which free-body diagram correctly represents the forces on the book?
   Answer: Forces: $mg$ downward; normal force upward; tension 6.0 N to the right. This question assesses the skill of identifying forces and constructing free-body diagrams in AP Physics 1. To create a correct free-body diagram, select the book as the system and identify all external forces acting on it. The real forces include the gravitational force mg downward from Earth, the normal force upward from the table, and the tension force of 6.0 N to the right from the string. No frictional force is present since friction is negligible, and there is no additional force in the direction of motion as acceleration results from the net force, not an extra force. Choice C is incorrect because it includes an extra force in the direction of motion, which is a common misconception but not a real force; motion does not require a separate force beyond the existing unbalanced forces. Always isolate the object and list only contact and field forces acting on it, ensuring no fictitious forces like 'force of acceleration' are included.
10. A $3.0\,\text{kg}$ crate rests on a horizontal floor. A person pulls horizontally to the right, but the crate does not move. Static friction is present. Which horizontal forces act on the crate?
    Answer: Applied pull to the right and static friction to the left (equal in magnitude) This question tests your ability to identify forces in a free-body diagram for a static equilibrium situation. The crate experiences an applied pull to the right and static friction to the left, which must be equal in magnitude since the crate remains at rest. Weight acts downward and normal force acts upward (these vertical forces aren't asked about but are present). Choice D incorrectly mentions a "reaction force" on the crate itself - Newton's third law pairs act on different objects, not the same object. The key strategy is that for an object at rest, all forces must balance, and static friction adjusts to match the applied force up to its maximum value.
11. A 1.0 kg mass hangs from a vertical spring and is momentarily at rest while moving upward; at that instant it is accelerating upward. Air resistance is negligible. Which forces act on the mass? Stem: Which free-body diagram correctly represents the forces on the hanging mass?
    Answer: Forces: spring force upward; weight $mg$ downward. This question assesses the skill of identifying forces and constructing free-body diagrams in AP Physics 1. Select the mass as the system and identify external forces from its environment. The real forces are the spring force upward from the spring and the gravitational force mg downward from Earth. At the instant it's momentarily at rest but accelerating upward, the spring force exceeds mg, resulting in a net upward force, but no additional force is present. Choice A is incorrect because it adds an extra upward force due to acceleration, but acceleration is the result of the imbalance between the real spring and weight forces, not a separate force. For oscillatory systems, include only elastic and gravitational forces in the free-body diagram and analyze net force for acceleration at specific points.
12. A block is pressed against a vertical wall by a horizontal push and remains at rest. Static friction is present between block and wall. The push is horizontal. Which forces act on the block?
    Answer: Weight downward, applied push into wall, normal force from wall, and static friction upward This question examines free-body diagrams for objects in static equilibrium against vertical surfaces with friction. Choose the block as the system and list external forces from contacts. The forces are weight downward, the applied horizontal push into the wall, normal force from the wall outward, and static friction upward opposing weight to prevent sliding. Equilibrium requires friction to balance weight vertically and normal to balance the push horizontally. Choice B is incorrect because it shows friction downward, which would not counteract weight and allow the block to fall. For such scenarios, ensure frictional forces are directed to oppose potential motion, and verify balance in all directions for rest conditions.
13. A block is held at rest against a vertical wall by a horizontal push to the right. Static friction is present. Which forces act on the block?
    Answer: Weight downward, normal force from wall to the left, applied push to the right, static friction upward This problem involves analyzing forces on a block held against a vertical wall. To create a free-body diagram, we select the block as our system and identify all forces acting on it. The block experiences four forces: weight (mg) downward, the applied horizontal push to the right, the normal force from the wall pushing back to the left, and static friction acting upward to prevent the block from sliding down. Since the block is at rest, all forces must balance - the push equals the normal force horizontally, and friction equals weight vertically. Choice D incorrectly shows friction pointing downward, which would cause the block to accelerate downward rather than remain at rest. When an object is held against a vertical surface, friction acts to prevent sliding in the direction gravity would cause motion.
14. A $2.0\,\text{kg}$ book rests on a horizontal table. Friction is negligible. The book is at rest (no acceleration). Which forces act on the book?
    Answer: Weight $mg$ downward and normal force upward This problem tests your understanding of forces and free-body diagrams for objects at rest. When analyzing forces on an object, we must identify all real forces acting directly on that object - in this case, the book. The book experiences two forces: its weight (mg) acting downward due to Earth's gravitational pull, and the normal force from the table pushing upward on the book. Since the book is at rest with no acceleration, these forces must be balanced. Choice C incorrectly includes a "force in the direction of motion," but there is no motion and no such force exists - forces cause motion, not the other way around. Remember: for any object resting on a surface, always include weight downward and normal force perpendicular to the surface.
15. A $4.0\,\text{kg}$ sled is pulled across level snow by a rope angled $30^\circ$ above horizontal. The sled moves at constant velocity. Kinetic friction is present. Which forces act on the sled?
    Answer: Weight downward, normal force upward, tension along the rope, kinetic friction opposite the motion This question tests your ability to identify forces in a free-body diagram for an object being pulled at an angle. The sled experiences four forces: weight (downward), normal force (upward from the snow), tension (along the rope at 30° above horizontal), and kinetic friction (opposite to the motion, so backward along the surface). Since the sled moves at constant velocity, these forces are balanced. Choice B incorrectly states there's no normal force because the rope lifts the sled - the rope's vertical component reduces but doesn't eliminate the normal force. The key strategy is to include all forces and remember that angled forces have both horizontal and vertical components.
16. A $0.20\,\text{kg}$ ball is thrown straight upward and is moving upward but slowing down. Air resistance is negligible. Which forces act on the ball? Select the correct free-body diagram.
    Answer: Forces: weight $mg$ downward only. This problem requires identifying forces in a free-body diagram for a ball thrown upward while slowing down. When constructing a free-body diagram, we choose the ball as our object and include only forces that act directly on it. With negligible air resistance, the only force is weight (mg) acting downward due to Earth's gravitational pull. Choice A incorrectly includes an 'upward force due to the ball's upward motion,' but motion is not a force—it's a state that results from previous forces. The ball moves upward because it was thrown (past force), but once released, only gravity acts on it, causing it to slow down. The essential strategy is to distinguish between forces (interactions happening now) and motion (result of past forces), and remember that projectiles in flight experience only gravitational force when air resistance is negligible.
17. A $2.0\,\text{kg}$ box is pulled across a horizontal floor at constant velocity by a horizontal rope. Kinetic friction is present. Which forces act on the box? Select the correct free-body diagram.
    Answer: Forces: $mg$ downward, normal force upward, tension to the right, kinetic friction to the left. This problem requires identifying forces in a free-body diagram for a box being pulled at constant velocity. When drawing a free-body diagram, we choose the box as our object and include only forces that directly act on it. The forces are: weight (mg) acting downward due to gravity, normal force acting upward from the floor supporting the box, tension acting horizontally in the direction of the pull (to the right), and kinetic friction acting opposite to the direction of motion (to the left). Choice D incorrectly includes a 'force of motion' to the right, but motion is not a force—it's the result of forces. Since the box moves at constant velocity, the net force is zero, meaning tension and friction are equal and opposite. The key strategy is to identify only real forces from interactions with other objects (Earth, floor, rope) and never include fictitious forces like 'force of motion.'
18. A $6.0\,\text{kg}$ sled is pulled up a snowy incline at constant velocity by a rope parallel to the incline. Kinetic friction is present. Which forces act on the sled? Select the correct free-body diagram.
    Answer: Forces: weight $mg$ downward, normal force perpendicular to incline, tension up the incline, kinetic friction down the incline. This problem requires identifying forces in a free-body diagram for a sled pulled up an incline at constant velocity. When constructing a free-body diagram, we select the sled as our object and include only forces acting directly on it. The forces are: weight (mg) acting straight downward from gravity, normal force acting perpendicular to the incline surface, tension acting up the incline parallel to the surface from the rope, and kinetic friction acting down the incline opposite to the direction of motion. Choice D incorrectly includes a 'force of constant velocity,' but constant velocity is not a force—it's a state that occurs when forces are balanced. Since velocity is constant, the net force is zero, meaning tension up the incline equals the sum of friction and the component of weight down the incline. The key strategy is to recognize that kinetic friction always opposes motion direction and that constant velocity indicates balanced forces, not an additional force.
19. A $0.50\,\text{kg}$ cart on a level track is pulled to the right by a string and accelerates rightward. Friction is negligible. Which forces act on the cart?
    Answer: Weight downward, normal force upward, and tension to the right This question tests your ability to identify forces in a free-body diagram. For the cart on a frictionless track, we need to identify all real forces acting on it: weight (gravitational force downward), normal force (support force from the track upward), and tension (pulling force from the string to the right). Since friction is negligible, there is no friction force. Choice A incorrectly adds a "force of motion" which is not a real force - motion is the result of forces, not a force itself. The key strategy is to include only forces from physical interactions: gravity, contact forces (normal and friction), and forces from attached objects (tension).
20. A puck moves at constant velocity across level ice. Friction and air resistance are negligible. Which forces act on the puck?
    Answer: Weight $mg$ downward and normal force upward This problem tests understanding of forces on an object in uniform motion with no friction. When creating a free-body diagram, we choose the puck as our system and identify only real forces acting on it. The puck experiences two forces: its weight (mg) downward from gravity and the normal force upward from the ice surface. Since the puck moves at constant velocity with no friction or air resistance, there is no net force, and these vertical forces balance each other. Choice A incorrectly includes a "forward force in the direction of motion" - objects in motion don't require forces to maintain constant velocity, only to change velocity. Remember Newton's first law: an object at constant velocity has zero net force.

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