how do i solve this, i tried dividing the mass by the height, but its wrong
A 407-kg pile driver is raised 15 m above ground.
(a) How much work must be done to raise the pile driver?__kj
(b) How much work does gravity do on the driver as it is raised?__kj
(c) The driver is now dropped. How much work does gravity do on the driver as it falls?__ kJ
To solve these questions, we need to understand the concept of work and the formulas involved. In physics, work is defined as the force applied on an object multiplied by the displacement of the object in the direction of the force.
(a) To calculate the work done to raise the pile driver, we need to know the gravitational force acting on it and the height it is raised. The formula for work is:
Work = Force x Displacement x cos(θ)
In this case, the Force is the weight of the pile driver, which is given by the formula:
Force = mass x gravity
where gravity is the acceleration due to gravity, which is approximately 9.8 m/s^2. The Displacement is the height the pile driver is raised, given as 15 m.
Therefore, the formula becomes:
Work = (mass x gravity) x height
Substituting the given values:
Work = (407 kg x 9.8 m/s^2) x 15 m
You can now calculate the work in kilojoules by performing the calculation.
(b) The work done by gravity on the driver as it is raised is equal in magnitude but opposite in direction to the work done to raise the pile driver. So, the answer will be the same as in part (a), but with opposite sign.
(c) When the driver is dropped, we can find the work done by gravity using the same formula as in part (a), but with the opposite sign. The displacement is now the height from which the object falls.
Therefore, the formula becomes:
Work = -(mass x gravity) x height
Substituting the given values:
Work = -(407 kg x 9.8 m/s^2) x 15 m
Again, you can now calculate the work in kilojoules by performing the calculation.
Remember to pay attention to units and the sign conventions for work in each case.