Consider a system of an 85.0 kg man, his 20.5-kg dog, and the earth. The gravitational...

Consider a system of an 85.0 kg man, his 20.5-kg dog, and the earth. The gravitational potential energy of the system increases by 1.90 10³ J when the man climbs a spiral staircase from the first to the second floor of an apartment building. If his dog climbs a normal staircase from the same first floor to the second floor, by how much does the potential energy of the system increase (in J)?

Expert Solution

In the question, the value of the change of the potential energy is not very clear. The decimal point seems to be used in the wrong place. However, we will solve the problem using the values as provided.

The change in the potential energy does not depend on the path at all, it depends on the height and the mass. If a mass is raised by a height then change in the potential energy is , where is the gravitational acceleration.

To solve the problem let the height between the 1st and 2nd floor is .

Let the mass of the person is and the mass of the dog is .

Then change in the potential energy of the man is

and change in the potential energy for the dog for the same height is .

Hence we have,

If the dog climbed then change in his potential energy is 0.458483 J.

Hence the total change in the potential energy of the system when dog climbs is (1.90103+0.458483) J=2.359513 J.

genius_generous answered 1 year ago

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