A 0.135 kg ball is thrown straight up from 1.94m above the ground. Its initial vertical speed is 5.60 m/s. A short time later, it hits the ground. Calculate the total work done by the force of gravity during that time.
To calculate the total work done by the force of gravity, we need to determine the change in gravitational potential energy of the ball as it moves from its initial position to the ground.
The gravitational potential energy of an object near the surface of the Earth can be calculated using the formula:
PE = m * g * h
Where:
PE is the gravitational potential energy
m is the mass of the object
g is the acceleration due to gravity (approximately 9.8 m/s^2 near the surface of the Earth)
h is the height of the object above a reference point (in this case, the ground)
The change in gravitational potential energy (∆PE) as the ball falls from its initial height to the ground can be determined using the following formula:
∆PE = PE_final - PE_initial
Let's calculate it step by step:
Step 1: Calculate the initial potential energy:
PE_initial = m * g * h_initial
Given:
m = 0.135 kg (mass of the ball)
g = 9.8 m/s^2 (acceleration due to gravity)
h_initial = 1.94 m (initial height of the ball)
Substituting the values:
PE_initial = 0.135 kg * 9.8 m/s^2 * 1.94 m
Step 2: Calculate the final potential energy:
PE_final = m * g * h_final
Since the ball hits the ground (∆h = 0), the final height is 0. Therefore:
h_final = 0 m
Substituting the values:
PE_final = 0.135 kg * 9.8 m/s^2 * 0 m
Step 3: Calculate the change in potential energy (∆PE):
∆PE = PE_final - PE_initial
Substituting the values obtained in steps 1 and 2:
∆PE = (0.135 kg * 9.8 m/s^2 * 0 m) - (0.135 kg * 9.8 m/s^2 * 1.94 m)
Now, calculate the value of ∆PE to find the total work done by the force of gravity during that time.