QuestionJuly 13, 2025

5.27 A 45.0 kg crate of tools rests on a horizontal floor.You exert a gradually increasing horizontal push on it,and the crate just begins to move when your force exceeds 313 N. Then you must reduce your push to 208 N to keep it moving at a steady 25.0cm/s (a) What are the coef- ficients of static and kinetic friction between the crate and the floor? (b) What push must you exert to give it an acceleration of 1.10m/s^2 (c) Suppose you were performing the same experiment on the moon, where the acceleration due to gravity is 1.62m/s^2 (i) What magnitude push would cause it to move? (ii) What would its acceleration be if you maintained the push in part (b)?

5.27 A 45.0 kg crate of tools rests on a horizontal floor.You exert a gradually increasing horizontal push on it,and the crate just begins to move when your force exceeds 313 N. Then you must reduce your push to 208 N to keep it moving at a steady 25.0cm/s (a) What are the coef- ficients of static and kinetic friction between the crate and the floor? (b) What push must you exert to give it an acceleration of 1.10m/s^2 (c) Suppose you were performing the same experiment on the moon, where the acceleration due to gravity is 1.62m/s^2 (i) What magnitude push would cause it to move? (ii) What would its acceleration be if you maintained the push in part (b)?
5.27 A 45.0 kg crate of tools rests on a horizontal floor.You exert a gradually increasing horizontal push on it,and the crate just begins to move when your force exceeds 313 N. Then you must reduce your push to 208 N to keep it moving at a steady 25.0cm/s (a) What are the coef- ficients of static and kinetic friction between the crate and the floor? (b) What push must you exert to give it an acceleration of 1.10m/s^2 (c) Suppose you were performing the same experiment on the moon, where the acceleration due to gravity is 1.62m/s^2 (i) What magnitude push would cause it to move? (ii) What would its acceleration be if you maintained the push in part (b)?

Solution
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Answer

(a) \mu_s = 0.707, \mu_k = 0.472 ### (b) F = 257.5 \, \text{N} ### (c)(i) f_s = 51.4 \, \text{N} ### (c)(ii) a = 5.12 \, \text{m/s}^2 Explanation 1. Calculate the coefficient of static friction Use **f_s = \mu_s N**. Here, f_s = 313 \, \text{N} and N = mg = 45.0 \, \text{kg} \times 9.81 \, \text{m/s}^2. Solve for \mu_s: \mu_s = \frac{313}{45.0 \times 9.81}. 2. Calculate the coefficient of kinetic friction Use **f_k = \mu_k N**. Here, f_k = 208 \, \text{N}. Solve for \mu_k: \mu_k = \frac{208}{45.0 \times 9.81}. 3. Calculate the push for acceleration on Earth Use **F = ma + f_k**. Here, a = 1.10 \, \text{m/s}^2, m = 45.0 \, \text{kg}, and f_k = 208 \, \text{N}. Solve for F: F = 45.0 \times 1.10 + 208. 4. Calculate the push to move the crate on the Moon Use **f_s = \mu_s N_{\text{moon}}**. Here, N_{\text{moon}} = mg_{\text{moon}} = 45.0 \, \text{kg} \times 1.62 \, \text{m/s}^2. Solve for f_s: f_s = \mu_s \times 45.0 \times 1.62. 5. Calculate the acceleration on the Moon with given push Use **a = \frac{F - f_k}{m}**. Here, F is from Step 3, and f_k = \mu_k \times 45.0 \times 1.62. Solve for a: a = \frac{F - f_k}{45.0}.

Explanation

1. Calculate the coefficient of static friction<br /> Use **$f_s = \mu_s N$**. Here, $f_s = 313 \, \text{N}$ and $N = mg = 45.0 \, \text{kg} \times 9.81 \, \text{m/s}^2$. Solve for $\mu_s$: $\mu_s = \frac{313}{45.0 \times 9.81}$.<br /><br />2. Calculate the coefficient of kinetic friction<br /> Use **$f_k = \mu_k N$**. Here, $f_k = 208 \, \text{N}$. Solve for $\mu_k$: $\mu_k = \frac{208}{45.0 \times 9.81}$.<br /><br />3. Calculate the push for acceleration on Earth<br /> Use **$F = ma + f_k$**. Here, $a = 1.10 \, \text{m/s}^2$, $m = 45.0 \, \text{kg}$, and $f_k = 208 \, \text{N}$. Solve for $F$: $F = 45.0 \times 1.10 + 208$.<br /><br />4. Calculate the push to move the crate on the Moon<br /> Use **$f_s = \mu_s N_{\text{moon}}$**. Here, $N_{\text{moon}} = mg_{\text{moon}} = 45.0 \, \text{kg} \times 1.62 \, \text{m/s}^2$. Solve for $f_s$: $f_s = \mu_s \times 45.0 \times 1.62$.<br /><br />5. Calculate the acceleration on the Moon with given push<br /> Use **$a = \frac{F - f_k}{m}$**. Here, $F$ is from Step 3, and $f_k = \mu_k \times 45.0 \times 1.62$. Solve for $a$: $a = \frac{F - f_k}{45.0}$.
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