Question

A wooden chest is pulled across a level ship's deck by a force of 2.20E2 N. If the chest accelerates at 0.488 m/s² and coefficient of friction between the object and the deck is 0.310, what is the mass of the wooden chest?

Answer 1

Answer on Question #42925, Physics, Mechanics | Kinematics | Dynamics

A wooden chest is pulled across a level ship's deck by a force of 2.20E2 N. If the chest accelerates at $0.488 \, \text{m/s}^2$ and coefficient of friction between the object and the deck is 0.310, what is the mass of the wooden chest?

Solution:

The equation of motion is

$$F - F_{fr} = ma,$$

where force is $F = 2.20E2 \, \text{N}$, force of friction is $F_{fr} = \mu \text{N}$ ($N = \text{mg}$, $\mu = 0.310$ is the coefficient of kinetic friction), the acceleration is $a = 0.488 \, \text{m/s}^2$.

Thus,

$$F - \mu \text{mg} = ma$$ $$m = \frac{F}{a + \mu g}$$ $$m = \frac{220}{0.488 + 0.310 \cdot 9.81} = 62.3 \, \text{kg}$$

Answer: $m = 62.3 \, \text{kg}$

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