Kinetic and Static Friction Practice

Sample questions

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1. Sample 1difficulty 1/5

   A spring stretches $0.04~\text{m}$ when a $20~\text{N}$ force is applied. Its spring constant is

   • A

     $500~\text{N/m}$

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   • B

     $5~\text{N/m}$

   • C

     $80~\text{N/m}$

   • D

     $0.8~\text{N/m}$

   Why

   $F = k x \Rightarrow k = F/x = 20/0.04 = 500~\text{N/m}$.

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2. Sample 2difficulty 2/5

   An object is in static equilibrium under three forces shown. $F_1 = F_2$ and they each make $45^\circ$ with the vertical (above the object). Weight $W$ pulls straight down. The relation among the magnitudes is

   • A

     $F_1 = F_2 = W/\sqrt{2}$

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   • B

     $F_1 + F_2 = W$

   • C

     $F_1 = F_2 = W/2$

   • D

     $F_1 = F_2 = W$

   Why

   Vertical sum: $2 F_1 \cos 45^\circ = W \Rightarrow F_1 = W/\sqrt 2$.

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3. Sample 3difficulty 2/5

   A $10~\text{kg}$ crate sits on a floor with coefficient of static friction $\mu_s = 0.30$. Using $g \approx 10~\text{m/s}^2$, what is the minimum horizontal force needed to start it moving?

   • A

     $3~\text{N}$

   • B

     $10~\text{N}$

   • C

     $30~\text{N}$

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   • D

     $100~\text{N}$

   Why

   The applied force must exceed $f_{s,\max} = \mu_s m g = (0.30)(10)(10) = 30~\text{N}$.

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4. Sample 4difficulty 2/5

   A $5.0~\text{kg}$ block on rough ground ($\mu_k = 0.20$) is pulled by a horizontal $20~\text{N}$ force. Using $g \approx 10~\text{m/s}^2$, its acceleration is

   • A

     $0~\text{m/s}^2$

   • B

     $4.0~\text{m/s}^2$

   • C

     $5.0~\text{m/s}^2$

   • D

     $2.0~\text{m/s}^2$

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   Why

   Friction: $f_k = \mu_k m g = (0.20)(5)(10) = 10~\text{N}$. Net $20 - 10 = 10~\text{N}$. $a = 10/5 = 2.0~\text{m/s}^2$.

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5. Sample 5difficulty 2/5

   A $2~\text{kg}$ block sits on a $20^\circ$ incline with $\mu_s = 0.50$. Will the block slide on its own? (Use $g \approx 10~\text{m/s}^2$.)

   • A

     Cannot be determined without more information.

   • B

     No — static friction can hold it.

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   • C

     Only if pushed.

   • D

     Yes, with $a > 0$.

   Why

   $\tan 20^\circ \approx 0.36 < \mu_s = 0.50$, so static friction can support the block. (Slipping requires $\tan\theta > \mu_s$.)

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