Spring Forces Practice

Sample questions

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1. Sample 1difficulty 1/5

   A $10~\text{kg}$ object hangs from a vertical rope at rest. Using $g \approx 10~\text{m/s}^2$, the rope tension is

   • A

     $100~\text{N}$

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   • B

     $0$

   • C

     $10~\text{N}$

   • D

     $50~\text{N}$

   Why

   For equilibrium, $T = m g = (10)(10) = 100~\text{N}$.

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2. Sample 2difficulty 2/5

   Two identical spring scales (each ideal) are connected end-to-end and a $10~\text{kg}$ mass is hung from the bottom. Using $g \approx 10~\text{m/s}^2$, each scale reads

   • A

     $200~\text{N}$

   • B

     Different values for each

   • C

     $100~\text{N}$

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   • D

     $50~\text{N}$

   Why

   Both scales are in series with the load and have the same tension everywhere along the rope: each reads $W = 100~\text{N}$.

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3. Sample 3difficulty 2/5

   The cable of the elevator above snaps and the cabin falls freely. What does the scale now read?

   • A

     $600~\text{N}$

   • B

     $300~\text{N}$

   • C

     $60~\text{N}$

   • D

     $0~\text{N}$

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   Why

   In free fall $a = -g$, giving $N = m(g + a) = m(g - g) = 0~\text{N}$ — the familiar "weightlessness" result.

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4. Sample 4difficulty 2/5

   A $3~\text{kg}$ mass hangs in equilibrium from a spring with $k = 150~\text{N/m}$. Using $g \approx 10~\text{m/s}^2$, the stretch from natural length is

   • A

     $0.15~\text{m}$

   • B

     $0.05~\text{m}$

   • C

     $0.20~\text{m}$

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   • D

     $0.30~\text{m}$

   Why

   $k x = m g \Rightarrow x = 30/150 = 0.20~\text{m}$.

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5. Sample 5difficulty 3/5

   Two identical springs (each $k$) connected in <strong>series</strong> behave as a single equivalent spring of constant

   • A

     $4k$

   • B

     $2k$

   • C

     $k/2$

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   • D

     $k$

   Why

   Total stretch under force $F$: $x = F/k + F/k = 2 F/k$, so $k_\text{eq} = F/x = k/2$.

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