By how much does the KE of a mass of 4 kg change as the elevation of the mass changes by 1.5 meters, assuming that the only force acting on the mass is gravitational? What is the associated PE change?
If we raise an object we do work in order to raise it. If we then drop it the work we did in raising it comes back to us in the form of energy of motion--kinetic energy. In this sense the raise object has a gravitational potential energy, which turns out to be equal to the work we did to raise it.
The PE change is the work that must be done against gravity as the object changes elevation. The force exerted on the object by gravity is its weight
An equal and opposite force is required to do the work against gravity.
- work against gravity = 39.2 Newtons * 1.5 meters = 58.8 Joules.
The work done by the system against gravity is equal to the change in its gravitational PE.
If no other forces act on the system, then this gravitational PE must come at the expense of the system’s KE, so the KE of the system changes by
When a system does work against gravitational forces, this work is recoverable
The work required to change the elevation of an object by `dy is equal to the product of the force exerted against gravity and `dy.
weight = m * g,
work against gravity = m g `dy.
If no forces other than gravity act on the object, then the work required to increase the elevation must come at the expense of its KE.
In many situations PE is the 'stored energy' that results from doing work against a conservative force--e.g., gravity or an elastic restoring force.
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