This question focuses on work and energy. Remember, energy is something that can

Question

This question focuses on work and energy. Remember, energy is something that can be transferred.

a. How much work is done against gravity by a 70.0-kg person climbing up a 2.00-m high staircase at constant velocity of 1.00 m/s? The person moves 4.00 m to the right as well as 2.00 m up while climbing the stairs. Explain.
b. What is the gravitational potential energy of a 32.4-kg object at rest on a plane inclined at an angle of 30° to the horizontal a distance 10.00 m up the plane? How do you know this?
c. Assuming the plane of (b) is frictionless, if the object is released, what kinetic energy will it have when it reaches the bottom of the plane? How do you know this?

Explanation / Answer

a. work done against gravity is... = 70x9.8x2= 1372J
4 m is not counted as the 4 movement is in horizontal direction and is therefore not against gravity. There is only 2m movement in vertical direction.

b. Gravitational potential energy = 70x 9.8 x10x sin30o

                                                 = 3430 J

This is known by the formula (mgh)........eq(i)

c. when the object reaches the bottom of the plane the kinetic energy becomes 3430J same as answer no b

This follows from the law of conservation of energy. The potential energy is completely converted to kinetic energy. Kinetic energy initially was zero as the object was at rest. At the bottom the potential energy became zero as the 'h' in eq(i) becomes zero.

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