A 0.267kg ball is thrown straight up from 2.20m above the ground. Its initial vertical speed is 9.20m/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 during the time the ball is in the air, we need to determine the change in the ball's gravitational potential energy.

The formula for calculating gravitational potential energy is given by U = mgh, where U is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.

In this case, the ball is thrown straight up, so we need to consider the initial height and the final height when calculating the potential energy change.

Given:
Mass of the ball, m = 0.267 kg
Initial vertical speed, v_i = 9.20 m/s
Initial height, h_i = 2.20 m
Final height, h_f = 0 (since it hits the ground)

First, we need to calculate the initial potential energy (U_i) and the final potential energy (U_f) using the formula:

U_i = m * g * h_i
U_f = m * g * h_f

where g is the acceleration due to gravity, which is approximately 9.8 m/s².

U_i = 0.267 kg * 9.8 m/s² * 2.20 m = 5.798 J
U_f = 0.267 kg * 9.8 m/s² * 0 m = 0 J

Next, we calculate the change in potential energy:

ΔU = U_f - U_i

ΔU = 0 J - 5.798 J = -5.798 J

The negative sign indicates that the potential energy has decreased.

Since work done is equal to the change in potential energy, we have:

Work done by gravity = ΔU

Therefore, the total work done by the force of gravity is approximately -5.798 Joules.

work done by gravity= mgh= .267*g*2.20