Question(I) The head of a hammer with a mass of 1.2 kg is allowed to fall onto a nail from a height of 0.65 m . What is the maximum amount of work it could do on the nail? Why do people not just "let it fall" but add their own force to the hammer as it falls?
Studdy Solution
STEP 1
1. The hammer head has a mass of 1.2 kg.
2. It falls from a height of 0.65 m.
3. We are assuming no air resistance or other energy losses.
4. We are calculating the maximum work done on the nail, which occurs when all potential energy is converted to work.
5. The gravitational acceleration is .
STEP 2
1. Calculate the gravitational potential energy of the hammer head at the initial height.
2. Determine the maximum work done on the nail.
3. Explain why additional force is applied to the hammer.
STEP 3
Calculate the gravitational potential energy (GPE) of the hammer head at the initial height using the formula:
where:
- (mass of the hammer head),
- (acceleration due to gravity),
- (height).
STEP 4
Calculate the value:
STEP 5
The maximum work done on the nail is equal to the gravitational potential energy calculated, assuming no energy losses:
STEP 6
Explain why additional force is applied to the hammer:
People add their own force to the hammer as it falls to increase the total energy transferred to the nail. By applying additional force, they increase the kinetic energy of the hammer head beyond what is provided by gravity alone, allowing the hammer to do more work on the nail, driving it in more effectively.
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