In this worksheet, we will practice relating forces perpendicular to a surface, kinetic friction coefficients of surfaces, and kinetic frictional forces.

**Q2: **

Two blocks connected by a string are pulled across a
horizontal surface by a force applied to one of the blocks,
as shown below. The coefficient of kinetic friction between
the blocks and the surface is 0.25. If each block has an
acceleration of 2.0 m/s^{2} to the right, what is the
magnitude of the applied force?

**Q3: **

A hockey puck at rest is hit. After being hit, the puck is shot across an ice-covered pond at a speed of 40 m/s. The puck comes to rest after moving a distance of 30 m across the ice. Find the magnitude of the average friction force on the puck.

**Q4: **

A machine at a post office sends box-shaped packages out of a chute and down a waxed wood-surfaced ramp that has a coefficient of friction 0.100 with the packages. Air resistance is negligible in this situation.

Calculate the acceleration of a package heading down a slope.

Find the angle of the slope down which a package could move at a constant velocity.

**Q5: **

A contestant in a winter sporting event pulls a 45.0 kg mass block of ice across a frozen lake with a rope over his shoulder. The rope makes a angle above the horizontal.

Calculate the magnitude of the minimum force that the contestant must exert to start the block moving. The coefficient of static friction between the ice block and the frozen lake is 0.100.

Calculate the magnitude of the block’s acceleration once it starts to move, assuming that the force needed to start the block moving is maintained. The coefficient of kinetic friction between the ice block and the frozen lake is 0.0300.

**Q6: **

A box of mass 12.4 kg box slides from rest downwards along a 1.58-m-length ramp that is inclined at below the horizontal. The coefficient of kinetic friction between the box and ramp is 0.0346.

What is the magnitude of the box’s acceleration?

- A
3.74 m/s
^{2} - B
3.30 m/s
^{2} - C
3.87 m/s
^{2} - D
3.56 m/s
^{2} - E
4.12 m/s
^{2}

What is the speed of the box at the bottom of the ramp?

- A 3.36 m/s
- B 5.11 m/s
- C 3.50 m/s
- D 2.37 m/s
- E 5.56 m/s

**Q7: **

A mechanic tries to insert a dry steel piston into a steel cylinder. Cylinder and piston are both horizontally aligned. A force of N is required to insert the piston.

What normal force was exerted on the piston when it was inserted? Use 0.300 for the value of the coefficient of kinetic friction of the piston and the cylinder.

The mechanic inserts an identical piston into an identical cylinder, but this time he oils the piston first. The oiled piston and cylinder have a coefficient of kinetic friction of 0.0300. What magnitude force does the mechanic need to apply while inserting the piston?

**Q8: **

Block 2 slides along a frictionless table as block 1 falls, as shown. Both blocks are attached by a frictionless pulley. Assume that both blocks start at rest and that the pulley has negligible mass. The mass of Block 1 is and the mass of Block 2 is . Find the speed of the blocks after they have each moved 2.0 m.

**Q9: **

A sled plus its passenger has a total mass of 42 kg. The sled is pulled across 26 m of snow at constant velocity by a force applied at an angle above the horizontal. The coefficient of friction between the sled and the snow is 0.16. Assume that the direction of the sled’s motion corresponds to positive displacement.

How much work does the applied force do on the sled?

How much work is done on the sled by friction?

**Q10: **

A steel crate with a mass of 145 kg rests on ice. There is a coefficient of static friction of 0.400 between the steel and the ice.

What is the maximum horizontal force that can be exerted on the crate without moving the crate?

The crate is pushed with a force that exceeds by a negligible amount the maximum force that can be exerted without moving the crate. The coefficient of kinetic friction between the steel and the ice is 0.0200. What magnitude of acceleration of the crate does this force produce?

**Q11: **

A horizontal force is applied to move a 5.00-kg-mass box a distance of 10.0 cm along a horizontal surface that has a coefficient of kinetic friction of with the box.

Find the work done on the box by the applied horizontal force during the box’s motion.

Find the work done on the box by the frictional force during the box’s motion.

Find the magnitude of the net force that acts on the box during its motion.

**Q12: **

A sled plus passenger have a total mass of 50.0 kg. The sled is pushed a distance of 20.0 m in the positive -direction across the snow at constant velocity by a force that is directed below the horizontal.

Calculate the work done on the sled by the applied force.

Calculate the work done on the sled by the force of friction.

Calculate the total work done on the sled over the 20 m distance.

**Q13: **

A block is given a short push and then it slides with constant friction across a horizontal floor. Which statement best explains the direction of the force that friction applies on the moving block?

- AFriction will be in the same direction as the block’s motion because thermal energy generated at the interface between the block and the floor adds kinetic energy to the block.
- BFriction will be in the same direction as the block’s motion because molecular interactions between the block and the floor will deform the block in the direction of its motion.
- CFriction will be in the opposite direction to the block’s motion because thermal energy generated at the interface between the block and the floor converts some of the block’s kinetic energy to potential energy.
- DFriction will be in the opposite direction to the block’s motion because molecular interactions between the block and the floor will deform the block in the opposite direction to its motion.

**Q14: **

A 3.00 kg block slides down a ramp which is at an incline of . The friction force between the block and the ramp is 5.20 N.

What is the coefficient of kinetic friction between the block and the ramp?

At what incline will the box slide at a constant velocity?

**Q15: **

A skier skies downward along a slope inclined at below the horizontal. The coefficient of kinetic friction between her skis and the snow is 0.100.

Calculate the acceleration of the skier heading down the hill.

Find the angle of the slope down which this skier could coast at a constant velocity. Ignore air resistance.

**Q16: **

A physics major is cooking breakfast when he notices that the frictional force between his steel spatula and his Teflon frying pan is only 0.200 N. If the coefficient of kinetic friction between steel and Teflon is 0.04, what is the normal force between the spatula and the pan?

**Q17: **

A block of mass 1.0 kg is at rest on a horizontal surface. The coefficient of static friction between the block and the surface is 0.50 and the coefficient of kinetic friction between the block and the surface is 0.40. A small force is applied to the block, which is steadily increased until the block starts to move along the surface when reaches the value .

What is the magnitude of ?

When is applied to the block, what is the magnitude of the block’s acceleration?

**Q18: **

A skier with a mass of 62 kg is sliding at a constant speed downwards along a snow-covered slope that is aligned at below the horizontal, producing a friction force of 45 N in the opposite direction to the motion. What is the coefficient of kinetic friction between the skis and the snow?

- A0.176
- B0.66
- C0.80
- D0.082
- E0.29