How hard surfaces can grip

Mathematics · Mechanics · ages 17-18

Name ______________________ Date ____________

A contact has normal reaction 60 N and static coefficient 0.4. Which statement gives the allowed range of the static friction magnitude f_s?
- f_s must always equal 24 N
- f_s can range from 0 to 24 N
- f_s can range from 0 to 60 N
- f_s must always equal 60 N
A block has normal reaction 40 N and static coefficient of friction 0.5. What is the maximum static friction?
- 10 N
- 20 N
- 40 N
A box is initially at rest on a fixed horizontal floor. Its static friction limit is 40 N. Its only other horizontal force is a 15 N push. What is the magnitude of the friction force?
- 40 N
- 0 N
- 15 N
A 10 kg box rests on a fixed horizontal floor. Weight and normal reaction are its only vertical forces. Take g = 10 N/kg and the static coefficient as 0.4. What is the maximum static friction in newtons?
Answer: ______________
An initially resting block has a 32 N static friction limit. Its only other horizontal force is a 32 N push. In the ideal model, the block can remain at rest at this limit. Is this statement true?
Circle one: True False
A block is initially at rest on a fixed horizontal floor. Its normal reaction is 50 N and its static coefficient is 0.6. Its only other horizontal force is a 35 N push. What happens?
- It starts sliding along the floor
- It remains at rest on the floor
- It immediately moves at steady speed
Mia says static friction always equals the static coefficient times the normal reaction. Is this claim true?
Circle one: True False
A block is initially at rest on a fixed horizontal floor. Horizontal pulls of 22 N right and 14 N left act. Its static friction limit is 30 N. There are no other horizontal forces except friction. What friction force acts?
- 8 N right
- 22 N left
- 8 N left
- 14 N right
A block remains at rest on a fixed horizontal floor under a 36 N horizontal pull. Friction is the only other horizontal force, and the normal reaction is 120 N. What is the smallest static coefficient consistent with this observation?
- 0.10
- 0.30
- 0.60
A block is already sliding right on a fixed horizontal floor. R = 80 N, mu_s = 0.5 and mu_k = 0.25. A constant 20 N push acts right. Friction is the only other horizontal force. What happens while it continues sliding?
- It accelerates right and gains speed
- It accelerates left and loses speed
- It stops at once and then moves left
- It moves right at constant speed

Answer key

For grown-ups. Fold this page away before handing over the rest.

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f_s can range from 0 to 24 N · The static limit is 0.4 times 60 = 24 N. The inequality allows any needed magnitude from zero up to 24 N.
20 N · The limit is the coefficient times the normal reaction: 0.5 times 40 N.
15 N · Static friction matches the push below the limit, so it supplies exactly 15 N.
40 · The normal reaction is 100 N, and 0.4 times 100 N is 40 N.
True · The required friction equals the static limit. Equality is allowed, so the block can remain at rest in limiting equilibrium.
It starts sliding along the floor · The static limit is 0.6 times 50 = 30 N. Static friction cannot balance the 35 N push, so sliding starts.
False · The claim is false. Static friction can be below its limit. Equality means limiting equilibrium, where rest is still possible.
8 N left · The pulls give a net 8 N right. This is below the 30 N static limit, so friction balances it with 8 N left.
0.30 · Balance requires 36 N of friction. The inequality 36 <= mu_s times 120 gives mu_s >= 0.30. The smallest possible coefficient is 0.30.
It moves right at constant speed · Sliding requires the kinetic coefficient. Friction is 20 N left, balancing the 20 N push. The resultant is zero, so velocity stays constant.