Newton's First Law (Translational Equilibrium) Practice

Sample questions

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1. Sample 1difficulty 1/5

   A book sits at rest on a table. Which statement correctly describes the forces on the book?

   • A

     The table pushes harder than gravity, but they balance.

   • B

     There are no forces on it because it's at rest.

   • C

     Only gravity acts on it.

   • D

     Gravity and the table's normal force act, summing to zero.

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   Why

   At rest, $F_\text{net} = 0$. Gravity (down) and normal force (up) are equal in magnitude and opposite in direction.

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2. Sample 2difficulty 2/5

   A $20~\text{N}$ box rests on a floor with $\mu_s = 0.40$. A horizontal push of $5~\text{N}$ is applied but the box doesn't move. What is the static friction on the box?

   • A

     $8~\text{N}$

   • B

     $5~\text{N}$

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   • C

     $0~\text{N}$

   • D

     $20~\text{N}$

   Why

   Static friction matches the applied force up to its maximum ($\mu_s N = 0.40 \times 20 = 8~\text{N}$). Here applied is only $5~\text{N}$, so $f_s = 5~\text{N}$.

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3. Sample 3difficulty 3/5

   A weight $W$ hangs from two ropes attached to a ceiling. Rope 1 makes $30^\circ$ with vertical and rope 2 makes $60^\circ$ with vertical. The tension $T_1$ in rope 1 (the more vertical one) is

   • A

     Larger than $T_2$.

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   • B

     Equal to $T_2$.

   • C

     Not enough info.

   • D

     Smaller than $T_2$.

   Why

   Vertical components must sum to $W$: $T_1\cos 30 + T_2\cos 60 = W$. Horizontal components cancel: $T_1\sin 30 = T_2\sin 60$, giving $T_2 = T_1\sin 30/\sin 60 = T_1/\sqrt 3 < T_1$.

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4. Sample 4difficulty 3/5

   A weight $W = 50~\text{N}$ hangs in equilibrium. String 1 makes $60^\circ$ below the horizontal ceiling and supports the weight. String 2 is horizontal. What is the tension in <strong>string 2</strong>?

   • A

     $29~\text{N}$

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   • B

     $25~\text{N}$

   • C

     $50~\text{N}$

   • D

     $58~\text{N}$

   Why

   Vertical: $T_1 \sin 60^\circ = W \Rightarrow T_1 = 50/0.866 \approx 58~\text{N}$. Horizontal: $T_2 = T_1 \cos 60^\circ \approx 58 \times 0.5 = 29~\text{N}$.

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5. Sample 5difficulty 3/5

   A $1.0~\text{kg}$ and a $4.0~\text{kg}$ block connected by a string on a frictionless surface are pulled by a $25~\text{N}$ force on the $4~\text{kg}$ block. What is the string tension?

   • A

     $20~\text{N}$

   • B

     $25~\text{N}$

   • C

     $10~\text{N}$

   • D

     $5~\text{N}$

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   Why

   System: $a = 25/5 = 5~\text{m/s}^2$. Isolate $1~\text{kg}$ block: $T = m a = (1)(5) = 5~\text{N}$.

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