In this problem, we will consider the following situation as depicted in the dia

Question

In this problem, we will consider the following situation as depicted in the diagram: (Figure 1) A block of mass m slides at a speedv along a horizontal smooth table. It next slides down a smooth ramp, descending a height h, and then slides along a horizontal rough floor, stopping eventually. Assume that the block slides slowly enough so that it does not lose contact with the supporting surfaces (table, ramp, or floor).

You will analyze the motion of the block at different moments using the law of conservation of energy.

Part D Where's the Energy? Using conservation of energy, find the speed vof the block at the bottom of the ramp Express your answer in terms of some or all the variables m, v, and h and any appropriate constants Learning Goal To understand how to apply the law of conservation of energy to situations with and without nonconservative forces acting The law of conservation of energy states the following In an isolated system the total energy remains constant. If the objects within the system interact through gravitational and elastic forces only, then the total mechanical energy is conserved Submit Hints My Answers Give Up Review Part The mechanical energy of a system is defined as the sum of kinetic energy K and potential energy U. For such systems in which no forces other than the gravitational and elastic forces do work, the law of conservation of energy can be written as Part E This question will be shown after you complete previous question(s) Figure 1 of 1 Part F This question will be shown after you complete previous question(s) Im Part G This question will be shown after you complete previous question(s) Part H

Explanation / Answer

Here ,

part A)

using the conservation of energy

final kinetic energy = initial kinetic energy + initial potential energy

0.5 * m * vb^2 = 0.5 * m * v^2 + m * g * h

vb^2 = v^2 + 2 * g * h

solving for vb

vb= sqrt(v^2 + 2 * g * h )

at the bottom , the speed of the bottom ramp is sqrt(v^2 + 2 * g * h )

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