# A tennis player hits a 58.0 g tennis ball so that it goes straight up and reaches a maximum height of 7.02 m .

Part A

How much work does gravity do on the ball on the way up?

Part B

How much work does gravity do on the ball on the way down?

## Part A: Well, gravity is always working hard, but on the way up, it does negative work on the tennis ball. How much work does it do? Well, let's just say gravity is not a fan of tennis, so it doesn't help the ball at all. Therefore, the work done by gravity on the way up is zero!

Part B: Now, on the way down, gravity is back in its element. It loves bringing stuff down to earth. So, how much work does gravity do on the way down? Well, it does negative work again because it's pulling the ball in the opposite direction of its motion. So, the work done by gravity on the way down is also zero! Gravity must be taking a vacation when it comes to tennis balls.

## To solve this problem, we can use the formula for work done by gravity:

Work done = force x distance

The force of gravity acting on the tennis ball is given by its weight, which can be calculated using the formula:

Weight = mass x acceleration due to gravity

In this case, the mass of the tennis ball is given as 58.0 g, which we need to convert to kilograms:

58.0 g = 0.058 kg (1 kg = 1000 g)

The acceleration due to gravity is approximately 9.8 m/s^2.

Part A:

To calculate the work done by gravity on the way up, we need to first determine the distance traveled by the ball. Since it reaches a maximum height of 7.02 m, the distance traveled on the way up is equal to half of that, or 3.51 m.

Using the formulas above, we can now calculate the work done by gravity on the way up:

Work done = force x distance

= Weight x distance

= (mass x acceleration due to gravity) x distance

= (0.058 kg x 9.8 m/s^2) x 3.51 m

Part B:

To calculate the work done by gravity on the way down, we can use the same formula as above since the force of gravity remains the same. However, the distance traveled on the way down is also 3.51 m.

Using the same formulas as in Part A, we can calculate the work done by gravity on the way down:

Work done = force x distance

= Weight x distance

= (mass x acceleration due to gravity) x distance

= (0.058 kg x 9.8 m/s^2) x 3.51 m

Therefore, the work done by gravity on the way up and on the way down is the same.

## To calculate the work done by gravity on the tennis ball, we need to use the equation:

Work = Force × Distance × cos(θ)

where:

- Work is the amount of work done by gravity,

- Force is the force exerted by gravity,

- Distance is the vertical distance traveled by the tennis ball, and

- θ is the angle between the force and displacement vectors (which is 180 degrees for downward motion and 0 degrees for upward motion).

Since the tennis ball goes straight up and straight down, the angle θ is 0 degrees for the upward motion and 180 degrees for the downward motion.

Now, let's solve each part of the question:

Part A: How much work does gravity do on the ball on the way up?

Since the ball goes straight up, the angle θ is 0 degrees. Therefore, cos(0) = 1.

The work done by gravity on the way up is given by:

Work = Force × Distance × cos(θ)

Now, we can calculate the work done by gravity using the formula:

Work = Weight × Distance × cos(θ)

The weight of the tennis ball can be calculated by multiplying its mass (58.0 g or 0.058 kg) by the acceleration due to gravity (9.8 m/s²):

Weight = Mass × Acceleration due to gravity

Work = (0.058 kg) × (9.8 m/s²) × (7.02 m) × cos(0)

Simplifying the equation:

Work = 0.058 kg × 9.8 m/s² × 7.02 m × 1

Part B: How much work does gravity do on the ball on the way down?

Since the tennis ball is coming back down, the angle θ is 180 degrees. Therefore, cos(180) = -1.

Using the same formula as before, the work done by gravity on the way down is:

Work = Weight × Distance × cos(θ)

Similarly, we can calculate the weight of the tennis ball and substitute it into the formula:

Work = (0.058 kg) × (9.8 m/s²) × (7.02 m) × cos(180)

Simplifying the equation:

Work = 0.058 kg × 9.8 m/s² × 7.02 m × -1

By evaluating these expressions, you can find the answers to both parts of the question.

## work done by gravity = force * distance

= - m g h

force in same direction as motion on the way down = + m g h

here

m = 0.058 kg

g = 9.81 m/s^2 or whatever your class uses or whatever planet you are on

h = 7.02 meters