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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

Find and compare the weight of a \(65-\mathrm{kg}\) man on Earth with the weight of the same man on (a) Mars, where \(g=3.7 \mathrm{N} / \mathrm{kg}.\) (b) Venus, where \(g=8.9 \mathrm{N} / \mathrm{kg} ;\) and (c) Earth's Moon, where \(g=1.6 \mathrm{N} / \mathrm{kg}.\)
A block of mass \(m_{1}=3.0 \mathrm{kg}\) rests on a frictionless horizontal surface. A second block of mass \(m_{2}=2.0 \mathrm{kg}\) hangs from an ideal cord of negligible mass that runs over an ideal pulley and then is connected to the first block. The blocks are released from rest. (a) Find the acceleration of the two blocks after they are released. (b) What is the velocity of the first block 1.2 s after the release of the blocks, assuming the first block does not run out of room on the table and the second block does not land on the floor? (c) How far has block 1 moved during the 1.2 -s interval? (d) What is the displacement of the blocks from their initial positions 0.40 s after they are released?
In a playground, two slides have different angles of incline \(\theta_{1}\) and \(\theta_{2}\left(\theta_{2}>\theta_{1}\right) .\) A child slides down the first at constant speed; on the second, his acceleration down the slide is \(a .\) Assume the coefficient of kinetic friction is the same for both slides. (a) Find \(a\) in terms of \(\theta_{1}, \theta_{2},\) and \(g.\) (b) Find the numerical value of \(a\) for \(\theta_{1}=45^{\circ}\) and \(\theta_{2}=61^{\circ}.\)
An airplane is cruising along in a horizontal level flight at a constant velocity, heading due west. (a) If the weight of the plane is $2.6 \times 10^{4} \mathrm{N},$ what is the net force on the plane? (b) With what force does the air push upward on the plane?
(a) What is the magnitude of the gravitational force that the Earth exerts on the Moon? (b) What is the magnitude of the gravitational force that the Moon exerts on the Earth? See the inside front and back covers for necessary information.
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