# Worksheet: Kinetic Friction

In this worksheet, we will practice analyzing the forces acting on objects on frictional surfaces when they move along these surfaces.

**Q1: **

A stone with a mass of 8.2 kg is initially at rest on a rough surface. The coefficient of static friction between the stone and the surface is 0.70, and the coefficient of kinetic friction between the stone and the surface is 0.60. A force is applied to the stone parallel to the surface that negligibly exceeds the force required to make the stone move across the surface. What is the magnitude of the acceleration of the stone across the surface?

**Q2: **

A cup is pushed so that it slides along a rough table top,
decelerating at
4.4 m/s^{2}.
What is the coefficient of kinetic
friction between the cup and the tabletop?

**Q3: **

A refrigerator with a mass of 105 kg is pushed a distance of 0.333 m across a rough horizontal surface. Moving the refrigerator dissipates 205 J of energy. What is the coefficient of kinetic friction of the refrigerator with the surface?

**Q4: **

An object in contact with a frictional surface has a coefficient of static friction and a coefficient of kinetic friction . What is the relationship between and for all examples of an object on a surface?

- A
- B
- C
- D

**Q5: **

A sled moves across horizontal ice, as shown in the diagram. The sled decelerates from 3.5 m/s to 2.5 m/s as it travels a distance . What is the magnitude of if the coefficient of kinetic friction of the sled with the ice is , where is the gravitational field strength of Earth?

**Q6: **

A box slides along a rough horizontal surface. The coefficient of static friction between the box and the surface is 0.82. The box dissipates 45 J of energy as it slides a distance of 2.4 m. What is the mass of the box?

**Q7: **

The graph shows the change in applied force on an object and the velocity of the object in the direction of the force. The object is on a surface that produces friction and the force is acting parallel to the surface. Air resistance is assumed to be negligible.

From after point I to before point II, is the applied force on the object larger than, smaller than, or equal to the force of friction on the object?

- ASmaller
- BLarger
- CEqual

From after point II to before point III, is the applied force on the object larger than, smaller than, or equal to the force of friction on the object?

- ASmaller
- BEqual
- CLarger

From after point III to point IV, is the applied force on the object larger than, smaller than, or equal to the force of friction on the object?

- AEqual
- BLarger
- CSmaller

**Q8: **

A sofa has a mass of 95 kg. The sofa is pushed a distance of 0.55 m across a rough horizontal surface that has a coefficient of kinetic friction with the sofa of 0.66. How much work is done on the sofa to move it across the surface at a constant velocity?

**Q9: **

The graph shows the change in applied force on an object and the velocity of the object in the direction of the force. The object is on a horizontal surface and the force acts parallel to the surface. Air resistance is assumed to be negligible.

From after point I to before point II, is the magnitude of the friction between the object and the surface definitely zero, definitely nonzero, or possibly either zero or nonzero?

- AEither zero or nonzero
- BDefinitely zero
- CDefinitely nonzero

From after point II to before point III, is the magnitude of the friction between the object and the surface definitely zero, definitely nonzero, or possibly either zero or nonzero?

- AEither zero or nonzero
- BDefinitely nonzero
- CDefinitely zero

From after point III to before point IV, is the magnitude of the friction between the object and the surface definitely zero, definitely nonzero, or possibly either zero or nonzero?

- AEither zero or nonzero
- BDefinitely zero
- CDefinitely nonzero

**Q10: **

The graph shows the change in applied force on an object and the velocity of the object in the direction of the force. The object is on a surface that produces friction and the force acts parallel to the surface. After the object has traveled a short distance, it starts to move over a different surface that has different friction characteristics. Air resistance is assumed to be negligible.

Between which points on the graph is the force applied greater than the weight of the object multiplied by the coefficient of static friction between the object and the surface?

- AIII and IV
- BI and II
- CI and III
- DII and III
- EII and IV

Between which points on the graph is the force due to friction acting on the object equal to the applied force on the object?

- AII and IV
- BIII and IV
- CII and III
- DI and IV
- EI and II

What is the ratio of the coefficient of static friction of the object with the surface that it is initially in contact with to the coefficient of kinetic friction of the object with the new surface that it comes into contact with after moving a short distance?

- A
- B
- C
- D
- E1