A 0.157kg ball is thrown straight up from 1.81m above the ground. Its initial vertical speed is 10.40m/s. A short time later, it hits the ground. Calculate the total work done by the force of gravity during that time.
(ball weight, N)x (elevation change)
= 0.157*9.8*1.81 = 2.785 Joules
The initial speed does not matter.
Why did the ball bring a calculator to its physics exam? Because it wanted to calculate its "work-out" routine! Alright, let's get to work.
To calculate the total work done by gravity, we need to find the change in the ball's potential energy. The change in potential energy (ΔPE) is equal to the negative work done by gravity. We can calculate ΔPE using the formula:
ΔPE = m * g * Δh
Where:
m = mass of the ball = 0.157 kg
g = acceleration due to gravity = 9.8 m/s^2
Δh = change in height = final height - initial height
The initial height is 1.81 m, and the final height is 0 m (since it hits the ground). So, the change in height Δh = 0 - 1.81 = -1.81 m.
Now we can calculate the total work done by gravity:
ΔPE = m * g * Δh
ΔPE = 0.157 kg * 9.8 m/s^2 * (-1.81 m)
Calculating this, we find that the total work done by gravity during that time is approximately -2.87 Joules.
So, it seems like gravity didn't have much "work ethic" in this scenario. It actually did negative work, which means it took energy away from the ball rather than adding to it.
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 moves from its initial height to the ground.
The formula for gravitational potential energy (PE) is given by:
PE = m * g * h
where m is the mass of the ball, g is the acceleration due to gravity, and h is the change in height.
Given:
m = 0.157 kg (mass of the ball)
h = 1.81 m (initial height above the ground)
g = 9.8 m/s^2 (acceleration due to gravity)
PE_initial = m * g * h_initial
PE_final = m * g * h_final
Since the ball hits the ground, h_final = 0.
Therefore, the change in gravitational potential energy is:
ΔPE = PE_final - PE_initial
ΔPE = (m * g * h_final) - (m * g * h_initial)
ΔPE = (0.157 kg * 9.8 m/s^2 * 0) - (0.157 kg * 9.8 m/s^2 * 1.81 m)
Calculating the change in gravitational potential energy:
ΔPE = -2.7334 J
Since gravity is acting downward, the work done by the force of gravity is negative.
Therefore, the total work done by the force of gravity during that time is -2.7334 J.
To calculate the total work done by the force of gravity during the ball's motion, we need to find the change in gravitational potential energy.
The gravitational potential energy is given by the formula:
PE = mgh
Where:
PE is the gravitational potential energy,
m is the mass of the object (0.157kg),
g is the acceleration due to gravity (approximately 9.8 m/s^2), and
h is the change in height.
Since the ball is thrown straight up, from a height of 1.81m and returns to the ground, the change in height is equal to the initial height. So, h = 1.81m.
Now, we can calculate the gravitational potential energy at the initial height:
PE_initial = m * g * h_initial
= 0.157kg * 9.8 m/s^2 * 1.81m
Next, we need to find the final gravitational potential energy at the ground level. Since the ball hits the ground, its final height is zero.
So, PE_final = m * g * h_final
= 0.157kg * 9.8 m/s^2 * 0m
= 0
The change in gravitational potential energy is then given by:
ΔPE = PE_final - PE_initial
= 0 - 0.157kg * 9.8 m/s^2 * 1.81m
Finally, the total work done by the force of gravity during that time is equal to the change in gravitational potential energy, which can be calculated as:
Work done by gravity = -ΔPE
= - (0.157kg * 9.8 m/s^2 * 1.81m)
Therefore, the total work done by the force of gravity is equal to -2.79 Joules. The negative sign signifies that the work done by gravity is in the opposite direction of the motion of the ball.