High School Physics : Understanding Newton's Second Law

Example Questions

Example Question #1 : Newton's Laws

Which of the following is not a part of Newton's second law?

Force

Displacement

Mass

Acceleration

Displacement

Explanation:

Newton's 2nd law states . Therefore, all we need is a force, a mass, and an acceleration!

Example Question #1 : Newton's Laws

A block is pushed with  newtons of force. What other information do we need in order to find the acceleration of the block?

Mass

Initial velocity

Final velocity

Acceleration due to gravity

Work done on the block

Mass

Explanation:

Newton's second law states that .

If we know the force, , then we only need to know the mass, , in order to find acceleration.

Example Question #3 : Understanding Newton's Second Law

orange falls from a tree. What is the force of gravity on the orange?

Explanation:

Newton's second law states that:

We are given the mass of the orange and the acceleration; since we are looking at the force due to gravity, the acceleration will be the acceleration due to gravity. Use these given values to calculate the force.

Keep in mind that the force will be negative, since gravity acts in the downward direction.

Example Question #1 : Understanding Newton's Second Law

ball rests on a flat table. What is the normal force exerted on the ball by the table?

Explanation:

Newton's second law allows us to solve for the force of gravity on the ball:

Newton's third law tells us that the force of the ball on the table, due to gravity, will be equal and opposite to the normal force of the table on the ball.

Substitute the equation for force of gravity.

Now we can use the mass of the ball and the acceleration of gravity to solve for the normal force. First, convert the mass to kilograms. Then, use the equation to find the normal force.

Example Question #1 : Understanding Newton's Second Law

Which of these is necessary for there to be a non-zero net force?

Non-zero frictional force

Non-zero net torque

Non-zero net acceleration

An equal and opposite reaction

Non-zero net displacement

Non-zero net acceleration

Explanation:

Newton's second law states that force is a mass times an acceleration.

In order for a force to exist, there must be an acceleration applied to a mass. A force cannot exist on a massless object, nor can it exist without a net acceleration.

Newton's third law states that for every force on an object, there is an equal and opposite force from the object. These force frequently cancel out, however, and produce a net force of zero.

Example Question #1 : Linear Motion Principles

Which of these is not an example of Newtonian mechanics?

Explanation:

Newtonian mechanics apply to all objects of substantial mass travelling at significantly slower than the speed of light.

Newton's law of universal gravitation, Newton's second law, momentum, and the equation for mechanical energy all fall under Newtonian mechanics.

The mass-energy equivalence suggests that mass can change as the speed of an object (such as an electron) approaches the speed of light. Newtonian mechanics assume that mass is constant, and do not apply to objects approaching the speed of light.

Example Question #7 : Understanding Newton's Second Law

A pair of fuzzy dice is hanging by a cord from your rearview mirror.  While you are decelerating at a constant rate from  to rest in , what angle does the string make with the vertical and in what direction (toward or away from the windshield)?

45 degrees toward the windshield

61 degrees away from the windshield

61 degrees toward the windshield

29 degrees away from the windshield

29 degrees toward the windshield

29 degrees toward the windshield

Explanation:

When you are slowing down the car, the fuzzy dice want to keep moving forward.  Therefore the angle they make will be toward the windshield.  The force of tension on the fuzzy dice is what is holding them back with the car, keeping them from going through the windshield.  This tension force is comprised of two components.  The y-component of the tension is equal to the force of gravity acting on the fuzzy dice.  The x-component of the tension is equal to the force of the car slowing down.

The angle of the fuzzy dice is related to these two components through the trigonometric function tangent.

We can then use in the inverse tan function to determine the angle acting on the fuzzy dice.

Notice how the mass of the dice falls out of the equation

We can now plug in our values and solve.

Example Question #8 : Understanding Newton's Second Law

Two dogs pull on a  bone in opposite directions. If the first dog pulls with a force of  to the left and the other pulls with a force of  in the opposite direction, what will be the acceleration on the bone?

We need to know the masses of the dogs in order to solve

Explanation:

First we need to find the net force, which will be equal to the sum of the forces on the bone.

Since the forces are going in opposite directions, we know that one force will be negative (since force is a vector). Conventionally, right is assigned a positive directional value. The force to the left will be negative.

From here we can use Newton's second law to expand the force and solve for the acceleration, using the mass of the bone.

Example Question #9 : Understanding Newton's Second Law

Derek pushes a  crate along a rough surface with  of force. He observes that it is only accelerating at a rate of . What must the value of the force of friction be?

(Assume the only two forces acting on the object are friction and Derek).

Explanation:

Newton's second law states that  .

If Derek is pushing with  of force, then we should be able to solve for the acceleration of the  crate.

Derek observes that the crate is acceleration at a rate of , rather than the expected . An outside force is acting upon it to slow the acceleration.

The equation for the net force on the object is: . We also know, from Newton's second law, that F resultant=ma resultant, where the resultant force and acceleration are the values actually observed.

Plug in the information we've been given so far to find the force of friction.

Subtract  from both sides to find the force of friction.

Friction will be negative because it acts in the direction opposite to the force of Derek.

Example Question #10 : Understanding Newton's Second Law

If you push a  mass with the same force that you push a  mass from rest.

None of the above is true

The  mass accelerates 6 times faster than the  mass

Both masses accelerate at the same rate

The  mass accelerates 6 times faster than the  mass

The  mass accelerates 6 times faster than the  mass

Explanation:

Newton's second law states that force is a mass times an acceleration.

Since both masses have the same force acting on it, we can look at the relationship between mass and acceleration.  These two things are inversely proportional to one another.  As one increases, the other decreases.  Therefore the larger mass will have a smaller acceleration.  The smaller mass will have a larger acceleration.

Suppose that the force acting on both objects is .  We can confirm this by solving for the acceleration.

The smaller mass will accelerate 6 times faster than the smaller mass.