Hi I really need help with this question... please provide a step by step explanation with the answer because I need to understand it.
Thanks!
A 406-kg pile driver (the figure below) is raised 12 m above ground.
(a) How much work must be done to raise the pile driver? [Answer in KJ]
(b) How much work does gravity do on the driver as it is raised? [Answer in kJ]
(c) The driver is now dropped. How much work does gravity do on the driver as it falls? [Answer in kJ]
Sure! Let's solve each part of the question step by step.
(a) To find the work done to raise the pile driver, we need to calculate the gravitational potential energy. The formula for gravitational potential energy is:
Gravitational Potential Energy = m * g * h
Where:
m = mass (in kg) = 406 kg (given in the question)
g = acceleration due to gravity = 9.8 m/s^2 (approximate value)
h = height (in m) = 12 m (given in the question)
Plugging the values into the formula:
Gravitational Potential Energy = 406 kg * 9.8 m/s^2 * 12 m
Work = Gravitational Potential Energy (since the work done is equal to the change in potential energy)
Now we can calculate the work by multiplying the expression:
Work = 406 kg * 9.8 m/s^2 * 12 m
Calculating the expression gives us the work in joules. To convert it to kilojoules, divide the value by 1000 since 1 kilojoule (kJ) is equal to 1000 joules.
So, the work done to raise the pile driver is:
Work = (406 kg * 9.8 m/s^2 * 12 m) / 1000 kJ
Now you can simply calculate the expression above to get the answer in kilojoules.
(b) To find the work done by gravity as the driver is raised, we can use the same formula for gravitational potential energy:
Work = Gravitational Potential Energy
Since the driver is being raised, the work done by gravity is negative (gravity acts in the downward direction opposite to the displacement). Therefore, the work done by gravity is equal to the negative of the gravitational potential energy:
Negative Work by Gravity = - Gravitational Potential Energy
We've already calculated the gravitational potential energy in part (a) as:
Gravitational Potential Energy = 406 kg * 9.8 m/s^2 * 12 m
So, the work done by gravity is:
Negative Work by Gravity = - (406 kg * 9.8 m/s^2 * 12 m)
Calculate the expression to get the answer in joules, and then divide by 1000 to convert it to kilojoules.
(c) When the driver is dropped, the work done by gravity is again negative since gravity acts in the downward direction opposite to the displacement. The work done by gravity is equal to the negative of the gravitational potential energy in this case as well.
We can use the same formula for gravitational potential energy:
Work = Gravitational Potential Energy
So, the work done by gravity as the driver falls is:
Negative Work by Gravity = - (406 kg * 9.8 m/s^2 * 12 m)
Calculate the expression to get the answer in joules, and then divide by 1000 to convert it to kilojoules.
That's it! Follow these steps for each part of the question to find the answers in kilojoules.