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Chapter 5: Problem 1

Which of the following is a correct unit of energy? a) \(\mathrm{kg} \mathrm{m} / \mathrm{s}^{2}\) c) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) e) \(\mathrm{kg}^{2} \mathrm{~m}^{2} / \mathrm{s}^{2}\) b) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}\) d) \(\mathrm{kg}^{2} \mathrm{~m} / \mathrm{s}^{2}\)

Short Answer

Expert verified
Answer: The correct unit of energy is c) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\).

Step by step solution

01

Define the Joule (J)

We know that the SI unit of energy is the Joule (J), named after the English physicist James Prescott Joule. It can be defined as the work done by a one Newton (N) force through a distance of one meter. In other words, 1 Joule = 1 N × 1 m. We also know that 1 N = \(\mathrm{kg} \mathrm{m} / \mathrm{s}^{2}\), which makes 1 J = \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\). Now, we are ready to compare each unit to this Joule unit.
02

Comparing the given choices

We will now compare each of the given options to the Joule's unit: a) \(\mathrm{kg} \mathrm{m} / \mathrm{s}^{2}\) - This is the unit for force (Newtons), not energy. c) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) - This matches the unit for Joules (energy). e) \(\mathrm{kg}^{2} \mathrm{~m}^{2} / \mathrm{s}^{2}\) - This does not match the unit for Joules (energy). b) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}\) - This is the unit for angular momentum, not energy. d) \(\mathrm{kg}^{2} \mathrm{~m} / \mathrm{s}^{2}\) - This does not match the unit for Joules (energy).
03

Identify the correct unit

From the comparison of each given option, it is evident that option c) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\) matches the Joule's unit for energy. Therefore, the correct unit of energy is: c) \(\mathrm{kg} \mathrm{m}^{2} / \mathrm{s}^{2}\).

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Most popular questions from this chapter

An \(800-\mathrm{N}\) box is pushed up an inclined plane that is \(4.0 \mathrm{~m}\) long. It requires \(3200 \mathrm{~J}\) of work to get the box to the top of the plane, which is \(2.0 \mathrm{~m}\) above the base. What is the magnitude of the average friction force on the box? (Assume the box starts at rest and ends at rest.) a) \(0 \mathrm{~N}\) c) greater than \(400 \mathrm{~N}\) b) not zero but d) \(400 \mathrm{~N}\) less than \(400 \mathrm{~N}\) e) \(800 \mathrm{~N}\)

5.60 A man throws a rock of mass \(m=0.325 \mathrm{~kg}\) straight up into the air. In this process, his arm does a total amount of work \(W_{\text {net }}=115 \mathrm{~J}\) on the rock. Calculate the maximum distance, \(h\), above the man's throwing hand that the rock will travel.

A mother pulls her daughter, whose mass is \(20.0 \mathrm{~kg}\) and who is sitting on a swing with ropes of length \(3.50 \mathrm{~m}\), backward until the ropes make an angle of \(35.0^{\circ}\) with respect to the vertical. She then releases her daughter from rest. What is the speed of the daughter when the ropes make an angle of \(15.0^{\circ}\) with respect to the vertical?

At sea level, a nitrogen molecule in the air has an average kinetic energy of \(6.2 \cdot 10^{-21}\) J. Its mass is \(4.7 \cdot 10^{-26} \mathrm{~kg}\). If the molecule could shoot straight up without colliding with other molecules, how high would it rise? What percentage of the Earth's radius is this height? What is the molecule's initial speed? (Assume that you can use \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\); although we'll see in Chapter 12 that this assumption may not be justified for this situation.

An engine expends 40.0 hp in moving a car along a level track at a speed of \(15.0 \mathrm{~m} / \mathrm{s}\). How large is the total force acting on the car in the opposite direction of the motion of the car?
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