The Physics
Hypertextbook
Opus in profectus

# Friction

## Problems

### practice

1. A wooden pallet carrying a load of 600 kg rests on a wooden floor.
1. A forklift driver decides to push it without lifting it. What force must be applied to just get the pallet moving?
2. After a bit of time, the pallet begins to slide. How fast is the pallet moving after sliding under the same force you calculated in part a. for half a second?
3. If the forklift stops pushing, how far does the pallet slide before coming to a stop?
2. Determine the following quantities for a car driving on a level surface with a coefficient of static friction of 0.75 (¾) and a coefficient of kinetic friction of 0.67 (⅔).
1. Determine the car's maximum starting acceleration with and without "burning rubber". How do these two methods of starting a car compare?
2. Determine the car's minimum braking distance with normal brakes and antilock brakes as a function of initial speed. How do these two methods of stopping a car compare?
3. Write something different.
This tab-delimited text file contains the stopping distance data for 123 cars tested by Road & Track (paid link) magazine in 1998. Two initial speeds were used: 26.82 m/s (60 mph) and 35.76 m/s (80 mph). Use the data in this file and your favorite data analysis software to determine the coefficient of static friction of car tires on pavement.

### conceptual

1. In the classical model of friction, surface area does not affect the force of friction between two surfaces in contact. Given this statement, answer the following questions.
1. Ordinary car tires have tread. (Racing cars don't, but that's another problem.) Tread reduces surface area in contact with the road, but surface area is not a factor affecting friction. Adding a complex shape to the exterior of a tire increases the manufacturing cost. Nobody likes spending money unnecessarily. What's the point behind this design choice? Why do ordinary car tires have tread?
2. Skis are long and skinny. Snow boards are wide and short. The point behind both sports is to slip across the surface of the snow with relatively little friction. Why wear a piece of apparatus with a large surface area if surface area doesn't affect friction?

### numerical

1. A 100 kg physics teacher pushes a 1.0 kg physics textbook across a 222 kg physics demo table. The teacher applies 5.0 N of force to start the book sliding and 4.0 N to keep it sliding at a constant 0.30 m/s across the table.
1. Sketch a free body diagram showing all the forces acting on the book as the teacher pushes it.
2. What is the magnitude of the weight of the book?
3. What is the magnitude of the normal force of the table on the book?
4. What is the coefficient of static friction between the book and the table?
5. What is the coefficient of kinetic friction between the book and the table?
6. If the teacher stops pushing the book, what is the magnitude of the net force on the book?
7. What acceleration does the book have after the teacher stopped pushing it?
8. How far does the book slide before coming to rest?
2. A car driving on asphalt comes to a complete stop with locked brakes in 10 m. What was the initial speed of the car?
3. A 1500 kg car is driving on a dry, level asphalt road. A deer runs across the road in front of the car and the driver makes an emergency stop. The car skids to a complete stop with locked brakes in 10 m. The driver does not hit the deer.
1. Draw a free body diagram of the skidding car.
2. Determine the weight of the car.
3. Determine the normal force of the road on the car.
4. Determine the friction force of the road on the car while skidding.
5. Determine the net force on the car while skidding.
6. Determine the acceleration of the car while skidding.
7. Determine the velocity of the car at the instant the driver first locked the brakes.
8. If the speed of the car before the brakes were applied was greater than the value you calculated in part g, how would this affect the magnitude of the frictional force? Would it increase, decrease, or remain the same?
4. A 20,000 N car is driving on a wet, level road at 11.5 m/s. A deer runs across the road in front of the car and the driver makes an emergency stop in 7.6 m. The car has anti-lock brakes and stops without skidding. The driver does not hit the deer.
1. Draw a free body diagram of the stopping car.
2. Determine the car's mass.
3. Determine the normal force of the road on the car.
4. Determine the car's acceleration while stopping.
5. Determine the net force on the car while stopping.
6. Determine the static friction force of the road on the car while stopping.
7. Determine the coefficient of static friction between the car and the road.
8. How would the stopping distance of the car change if the road was dry? Would it increase, decrease, or remain the same?
5. A forklift is used to push a 12,500 N crate across a level floor at a constant velocity. The forklift pushes with 4000 N of force.
1. Sketch a free body diagram showing all the forces acting on the crate.
2. What is the mass of the crate?
3. What is the acceleration of the crate?
4. What is the net force on the crate?
5. What is the normal force of the crate on the ground?
6. What is the kinetic friction force between the crate and the floor?
7. What is the coefficient of kinetic friction between the crate and the floor?
8. What effect will increasing the speed of the forklift have on the force of friction between the crate and the floor? Will it increase, decrease, or remain the same?
6. A 15,500 N car driving on a dry asphalt road comes to a complete stop after skidding 10 m with the engine disengaged and the brakes locked.
1. Sketch a free body diagram showing all the forces acting on the car as it is braking.
2. What is the mass of the car?
3. What is the normal force of the road on the car?
4. What is the friction force between the car and the road?
5. What is the net force on the car as it is braking?
6. What is the acceleration of the car as it is braking?
7. What effect will reducing the initial speed of the car have on the force of friction between the car and the road?
8. What effect will reducing the initial speed of the car have on the braking distance? Will it increase, decrease, or remain the same?
7. A stunt double is being dragged along the ground at a constant velocity by a rope attached to a moving truck. The rope is parallel to the ground, the weight of the double is 640 N, and the coefficient of kinetic friction between the stunt double and the ground is 0.25.

Magnify

1. Sketch a free body diagram showing all the forces acting on the stunt double.
2. What is the mass of the stunt double?
3. What is the acceleration of the stunt double?
4. What is the net force on the stunt double?
5. What is the normal force of the stunt double on the ground?
6. What is the friction force between the stunt double and the ground?
7. What is the tension in the rope?
8. What effect will reducing the speed of the truck have on the force of friction between the stunt double and the ground? Will it increase, decrease, or remain the same?

### statistical

1. The table below shows some of the best and worst performing cars in an emergency braking test.
make
model
weight/mass initial speed braking distance
(lb) (kg) (mph) (m/s) (ft) (m)
Mercedes-Benz
E550 Coupe
3810 1728 80 35.8 252 76.8
Porsche
911 GT3
3075 1395 80 35.8 186 56.7
Volkswagen
Golf GTI 3-dr
3370 1529 60 26.8 143 43.6
Alfa Romeo
8C Competizione
3495 1585 60 26.8 105 32.0
1. Draw a free body diagram of a car in an emergency braking test.
2. For all four cars, determine the…
1. braking acceleration
2. coefficient of friction between the tires and test track
2. wood-wood.txt
A group of physics students measured the static and kinetic frictional forces as they dragged a wooden block across a wooden plank resting on a table. They placed weights on top of the block, which varied the normal force. Construct a graph with the frictional forces on the vertical axis and the normal force on the horizontal axis. Add a line of best fit and determine the static and kinetic coefficients of friction for wood on wood.
3. wood-stone.txt
A group of physics students connected a force sensor to a 2.0 kg wooden block and recorded the force they used to drag the block across a smooth, level stone table. They began the experiment by pulling lightly on the block with a gradually increasing force until the block started to move. Once the block started moving, they tried to pull it at a constant velocity (and were reasonably successful). The results of one trial were saved in this tab delimited text file. Use this data to determine the static and kinetic coefficients of friction for wood on stone.

### investigative

1. The horizontal force of the heel as it strikes the ground when a person is walking has been measured and found to be approximately 15% of a person's weight.
1. What minimum coefficient of static friction do shoes need to have to keep a person from slipping?
2. Wood, leather, and rubber have all been used as materials for the soles of shoes. Pick any one of these materials.
1. Identify a surface that people can walk on using a sole made from this material because they won't slip.
2. Identify a surface that people can't walk on using a sole made from this material because they will slip.
Provide a reference for the source of your information and summarize your findings in a table like the one below.
can walk/won't slip can't walk/will slip
μs
material
reference
Sole material: wood, leather, rubber (select one)