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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

Two railroad cars, each of mass \(7000 . \mathrm{kg}\) and traveling at \(90.0 \mathrm{~km} / \mathrm{h},\) collide head on and come to rest. How much mechanical energy is lost in this collision?

Supppose you pull a sled with a rope that makes an angle of \(30.0^{\circ}\) to the horizontal. How much work do you do if you pull with \(25.0 \mathrm{~N}\) of force and the sled moves \(25.0 \mathrm{~m} ?\)

A hammerhead of mass \(m=2.00 \mathrm{~kg}\) is allowed to fall onto a nail from a height \(h=0.400 \mathrm{~m} .\) Calculate the maximum amount of work it could do on the nail.

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.

A car of mass \(m\) accelerates from rest along a level straight track, not at constant acceleration but with constant engine power, \(P\). Assume that air resistance is negligible. a) Find the car's velocity as a function of time. b) A second car starts from rest alongside the first car on the same track, but maintains a constant acceleration. Which car takes the initial lead? Does the other car overtake it? If yes, write a formula for the distance from the starting point at which this happens. c) You are in a drag race, on a straight level track, with an opponent whose car maintains a constant acceleration of \(12.0 \mathrm{~m} / \mathrm{s}^{2} .\) Both cars have identical masses of \(1000 . \mathrm{kg} .\) The cars start together from rest. Air resistance is assumed to be negligible. Calculate the minimum power your engine needs for you to win the race, assuming the power output is constant and the distance to the finish line is \(0.250 \mathrm{mi}\)
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