### All MCAT Physical Resources

## Example Questions

### Example Question #12 : Work, Energy, And Power

A 5kg ball is attached to a 10m rope. The ball is held at a horizontal angle and allowed to fall freely with a pendulum-like motion. Assume there is no air resistance.

What is the velocity of the ball when it is at its lowest point?

**Possible Answers:**

**Correct answer:**

This problem becomes much easier if we use the law of conservation of energy. Because there is no friction involved, all of the ball's potential energy was converted into kinetic energy when falling through the pendulum arc. As a result, the velocity at the bottom of the swing can be determined using the equation below.

Because the potential energy at the bottom of the swing is zero (relative to the starting point), and the velocity at the top is zero, we can simplify the equation.

Since the string is 10m long, we know that the lowest point will be 10m below the starting point.

### Example Question #1 : Kinetic Energy

Two children are playing with sleds on a snow-covered hill. Sam weighs 50kg, and his sled weighs 10kg. Sally weighs 40kg, and her sled weighs 12kg. When they arrive, they climb up the hill using boots. Halfway up the 50-meter hill, Sally slips and rolls back down to the bottom. Sam continues climbing, and eventually Sally joins him at the top.

They then decide to sled down the hill, but disagree about who will go first.

Scenario 1:

Sam goes down the hill first, claiming that he will reach a higher velocity. If Sally had gone first, Sam says they could collide.

Scenario 2:

Sally goes down the hill first, claiming that she will experience lower friction and thus reach a higher velocity. If Sam had gone first, Sally says they could collide.

Scenario 3:

Unable to agree, Sam and Sally tether themselves with a rope and go down together.

If the hill is frictionless, and after both Sally and Sam reach the bottom of the hill traveling at maximum velocity, who has lost more potential energy?

**Possible Answers:**

They have lost an equal amount of potential energy

Sam, because he is traveling more slowly

Sam, because his mass is larger

Sally, because she is traveling faster

Sally, because she experiences less friction

**Correct answer:**

Sam, because his mass is larger

When they reach the bottom of the hill, Sam and Sally have both converted all of their potential energy into kinetic energy. We measured potential energy at 50m, so once they have lost 50m, the potential energy is 0, while the kinetic energy has reached maximum value. Because Sam has greater mass, he had more potential energy to convert to kinetic energy.

### Example Question #21 : Work, Energy, And Power

Two children are playing with sleds on a snow-covered hill. Sam weighs 50kg, and his sled weighs 10kg. Sally weighs 40kg, and her sled weighs 12kg. When they arrive, they climb up the hill using boots. Halfway up the 50-meter hill, Sally slips and rolls back down to the bottom. Sam continues climbing, and eventually Sally joins him at the top.

They then decide to sled down the hill, but disagree about who will go first.

Scenario 1:

Sam goes down the hill first, claiming that he will reach a higher velocity. If Sally had gone first, Sam says they could collide.

Scenario 2:

Sally goes down the hill first, claiming that she will experience lower friction and thus reach a higher velocity. If Sam had gone first, Sally says they could collide.

Scenario 3:

Unable to agree, Sam and Sally tether themselves with a rope and go down together.

After reaching maximum velocity at the bottom of a frictionless hill identical to the one in the question, Sam deploys a parachute. How much energy must the parachute dissipate before Sam comes to a stop?

**Possible Answers:**

30J

300kJ

30kJ

300J

30000kJ

**Correct answer:**

30kJ

The parachute must dissipate all of the kinetic energy that Sam has at the bottom of the hill, since there is no friction to slow him. He has 30kJ of energy, as per the equation PE = mgh.

PE = 60kg * 10m/s^{2 }* 50m = 30,000J = KE at the bottom of the hill

### Example Question #21 : Work, Energy, And Power

How much energy is required to a accelerate a block from rest to a final speed of ?

**Possible Answers:**

**Correct answer:**

From an energy stand-point, the block starts with zero kinetic energy and zero potential energy. At the end, the block still has zero potential energy, but has a non-zero kinetic energy. Assuming there is no friction, all energy added to the block have been converted to kinetic energy.

Using the change in velocity, we can solve for the energy used to move the block.

We are given our mass and the change in velocity, allowing us to solve for the change in kinetic energy.

### Example Question #22 : Work, Energy, And Power

What is the kinetic energy of a bullet moving at ?

**Possible Answers:**

**Correct answer:**

Kinetic energy is given by the formula:

We are given the mass of the bullet and its velocity, allowing us to calculate kinetic energy from this formula.

Work is often expressed in Newton-meters, but energy is usually expressed as Joules, although the units are equivalent.

### Example Question #1 : Kinetic Energy

Two children are playing on an icy lake. Child 1 weighs 50kg, and child 2 weighs 38kg. Child 1 has a backpack that weighs 10kg, and child 2 has a backpack that weighs 5kg.

Over the course of the afternoon, they collide many times. Four collisions are described below.

Collision 1:

Child 1 starts from the top of a ramp, and after going down, reaches the lake surface while going and subsequently slides into a stationary child 2. They remain linked together after the collision.

Collision 2:

Child 1 and child 2 are sliding in the same direction. Child 2, moving at , slides into child 1, moving at .

Collision 3:

The two children collide while traveling in opposite directions at each.

Collision 4:

The two children push off from one another’s back, and begin moving in exactly opposite directions. Child 2 moves with a velocity of .

In collision 1, imagine that child 2 was not present on the ice. How much energy would child 1 have to dissipate to the lake surface before he came to a stop? Ignore wind resistance.

**Possible Answers:**

**Correct answer:**

The amount of kinetic energy that child 1 has after she reaches the lake surface is the amount of energy she will dissipate to the lake before coming to a complete stop.

### Example Question #24 : Work, Energy, And Power

What is the kinetic energy of a 0.1kg projectile traveling at ?

**Possible Answers:**

**Correct answer:**

We can calculate the kinetic energy using the equation:

Use the given values for the mass and velocity to solve:

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