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Chapter 4: Problem 28

A large wooden crate is pushed along a smooth, frictionless surface by a force of \(100 \mathrm{N}\). The acceleration of the crate is measured to be $2.5 \mathrm{m} / \mathrm{s}^{2} .$ What is the mass of the crate?

Short Answer

Expert verified
Answer: The mass of the crate is 40 kg.

Step by step solution

01

Write down the given values and the formula

In this case, the given values are: Force (F) = \(100 \thinspace \mathrm{N}\) Acceleration (a) = \(2.5 \thinspace \mathrm{m/s^2}\) We need to find the mass (m) of the crate. The formula we will use is Newton's second law of motion: \(F = ma\)
02

Rearrange the formula to solve for mass

In order to find the mass, we need to rearrange the formula. We can do this by dividing both sides of the equation by acceleration (a): \(m = \dfrac{F}{a}\)
03

Substitute the given values and solve for mass

Now, we can plug in the given values of force and acceleration into the formula and solve for mass: \(m = \dfrac{100 \mathrm{N}}{2.5 \mathrm{m/s^2}}\) \(m = 40 \thinspace \mathrm{kg}\)
04

State the answer

The mass of the crate is \(40 \thinspace \mathrm{kg}\).

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Most popular questions from this chapter

Which of the following forces have an unlimited range: strong force, contact force, electromagnetic force, gravitational force?
A skier with a mass of \(63 \mathrm{kg}\) starts from rest and skis down an icy (frictionless) slope that has a length of \(50 \mathrm{m}\) at an angle of \(32^{\circ}\) with respect to the horizontal. At the bottom of the slope, the path levels out and becomes horizontal, the snow becomes less icy, and the skier begins to slow down, coming to rest in a distance of \(140 \mathrm{m}\) along the horizontal path. (a) What is the speed of the skier at the bottom of the slope? (b) What is the coefficient of kinetic friction between the skier and the horizontal surface?
A computer weighing \(87 \mathrm{N}\) rests on the horizontal surface of your desk. The coefficient of friction between the computer and the desk is $0.60 .$ (a) Draw an FBD for the computer. (b) What is the magnitude of the frictional force acting on the computer? (c) How hard would you have to push on it to get it to start to slide across the desk?
A woman who weighs \(600 \mathrm{N}\) sits on a chair with her feet on the floor and her arms resting on the chair's armrests. The chair weighs $100 \mathrm{N}\(. Each armrest exerts an upward force of \)25 \mathrm{N}$ on her arms. The seat of the chair exerts an upward force of \(500 \mathrm{N}\). (a) What force does the floor exert on her feet? (b) What force does the floor exert on the chair? (c) Consider the woman and the chair to be a single system. Draw an FBD for this system that includes all of the external forces acting on it.
Four identical spring scales, \(\mathrm{A}, \mathrm{B}, \mathrm{C},\) and \(\mathrm{D}\) are used to hang a \(220.0-\mathrm{N}\) sack of potatoes. (a) Assume the scales have negligible weights and all four scales show the same reading. What is the reading of each scale? (b) Suppose that each scale has a weight of \(5.0 \mathrm{N} .\) If scales \(\mathrm{B}\) and \(\mathrm{D}\) show the same reading, what is the reading of each scale?
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