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 find the change in gravitational potential energy of the ball.
The gravitational potential energy is given by the formula:
PE = m * g * h
Where:
PE is the gravitational potential energy
m is the mass of the ball (0.135 kg)
g is the acceleration due to gravity (9.8 m/s^2)
h is the height above the ground (1.94 m)
At the initial position, the ball has a gravitational potential energy of:
PE_initial = m * g * h_initial
At the final position (when the ball hits the ground), the height above the ground is zero, so the gravitational potential energy becomes:
PE_final = m * g * h_final
The change in gravitational potential energy is then:
ΔPE = PE_final - PE_initial
Substituting the values, we get:
ΔPE = (0.135 kg) * (9.8 m/s^2) * (0 m) - (0.135 kg) * (9.8 m/s^2) * (1.94 m)
Simplifying further:
ΔPE = -0.135 kg * 9.8 m/s^2 * 1.94 m
Calculating the result, we find:
ΔPE ≈ -2.62 J
Since the work done by gravity is equal to the change in potential energy, the total work done by the force of gravity during that time is approximately -2.62 Joules (J). Note that the negative sign indicates that the work done by gravity is in the opposite direction of the ball's displacement.
To calculate the total work done by the force of gravity, we need to find the change in gravitational potential energy of the ball as it falls from its initial height to the ground.
The gravitational potential energy can be calculated using the formula:
PE = m * g * h
where PE is the gravitational potential energy, m is the mass of the ball, g is the acceleration due to gravity, and h is the height.
In this case, the mass of the ball is 0.135 kg, the acceleration due to gravity is approximately 9.8 m/s², and the height is 1.94 m.
So, the initial gravitational potential energy of the ball is:
PE_initial = m * g * h
PE_initial = 0.135 kg * 9.8 m/s² * 1.94 m
To find the final gravitational potential energy, we need to calculate the height of the ball when it hits the ground. Since the ball was thrown straight up and then falls back down, the total height it travels is twice the initial height.
Total height = 2 * 1.94 m
Now we can calculate the final gravitational potential energy:
PE_final = m * g * h
PE_final = 0.135 kg * 9.8 m/s² * (2 * 1.94 m)
The change in gravitational potential energy is given by the difference between the initial and final potential energy:
Work = PE_final - PE_initial
Substituting the calculated values, we have:
Work = (0.135 kg * 9.8 m/s² * (2 * 1.94 m)) - (0.135 kg * 9.8 m/s² * 1.94 m)
Now you can calculate the total work done by the force of gravity by evaluating the expression.
h=v²/2g=5.6²/2•9.8 =1.6m.
Upward motion
W1=-mgh= - 0.135•9.8•1.6= - 2.12 J
Downward motion
W2= mg(H+h) = 0.135•9.8•(1.94+1.6) =4.68 J
W= W1+W2 = -2.12 +4.68 = 2.56 J.