# Worksheet: Conservative and Nonconservative Forces

In this worksheet, we will practice calculating the position, velocity, and kinetic energy of objects that experience variable forces.

**Q10: **

The force on a particle with a mass of 1.5 kg varies with position according to N. At a position m, the bodyβs speed is 3.7 m/s in the positive -direction.

Calculate the mechanical energy of the particle, taking the origin as the point of zero potential.

Calculate the particleβs velocity at the position m, taking the origin as the point of zero potential.

Calculate the mechanical energy of the particle, taking the position m as the point of zero potential.

Calculate the particleβs velocity at the position m, taking the position m as the point of zero potential.

**Q16: **

You are in a room in a basement with a smooth concrete floor and a nice rug. The rug is 3 m wide and 4 m long. You have to push a very heavy box from one corner of the rug to its opposite corner. The magnitude of friction between the box and the rug is 55 N, but the magnitude of friction between the box and the concrete floor is only 40 N. Will you do more work against friction going around the floor or across the rug? How much extra work would it take?

- AAround the floor, 280 J
- BAcross the rug, 5 J
- CAcross the rug, 275 J
- DAround the floor, 5 J
- EAround the floor, 275 J

**Q17: **

An 85.0 kg cross-country skier is climbing a slope at a constant speed of 1.50 m/s and encounters air resistance of 20.0 N.

Find his power output for work done against the gravitational force and air resistance.

What average force does he exert backward on the snow to accomplish this?

If he continues to exert the same force backward on the snow and to experience the same air resistance when he reaches a level area, how long will it take him to reach a velocity of 10.0 m/s?

**Q18: **

The force N and the force N, where and are constants with appropriate units.

If is the derivative of the -component of with respect to and is the derivative of the -component of with respect to , what is the ratio of to ?

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If is the derivative of the -component of with respect to and is the derivative of the -component of with respect to , what is the ratio of to ?

**Q20: **

The potential energy of a particle due to conservative forces acting on it is given by , where , and no nonconservative forces act on it. The particle is moving along the -axis and its total energy at is 2 J. At a point on the positive -axis, the particle has zero kinetic energy.

What is the value of ?

What magnitude force acts on the particle at ?

If the kinetic energy of the particle is 1 J at , what magnitude force acts on it at that point?

**Q21: **

A particle with a mass is suspended from a string of negligible mass and a length of 1.0 m, as shown in the diagram. The particle is displaced to a position where the taut string is at an angle of from the vertical, and the particle is released from rest at that position. The particle moves through an arc, where the lowest point of the arc is the point .

What is the instantaneous speed of the particle at point ?

What is the vertically upward displacement of the particle from point when its instantaneous speed is 0.81 m/s?

**Q23: **

The mechanical energy, , of an object, is equal to the sum of its kinetic energy, , and its potential energy,

The energy dissipated by non-conservative forces acting upon an object is the change in the mechanical energy, . A particle of mass 1 kg moves from point to point , and is acted upon by a non-conservative force as it does so, losing energy. If the object had a mechanical energy of 4 J at point , what value of potential energy, , must it have had in order to move at a constant velocity of 2 m/s between points and .

**Q24: **

The potential energy for a particle undergoing one-dimensional motion along the -axis is , where is measured in joules and is measured in meters. The particle has a constant mechanical energy J.

What positive region along the -axis is the particleβs motion confined to?

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What is the position of the stable equilibrium point on the positive -axis for the particle?

What positive region along the -axis is the particleβs motion confined to if its mechanical energy is a constant 0.25 J?

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