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Chapter 6: Problem 10

An automobile with a mass of \(1600 \mathrm{kg}\) has a speed of $30.0 \mathrm{m} / \mathrm{s} .$ What is its kinetic energy?

Short Answer

Expert verified
Answer: The kinetic energy of the automobile is 720,000 J.

Step by step solution

01

Identify the given values

Here, we are given the mass of the automobile, \(m = 1600 \mathrm{kg}\), and its speed, \(v = 30.0 \mathrm{m/s}\).
02

Write down the formula for kinetic energy

The formula for kinetic energy is given by: \(KE = \frac{1}{2}mv^2\).
03

Plug in the given values into the formula

Lets plug the given mass \(m\) and speed \(v\) into the formula of kinetic energy. Thereby, we can substitute \(m=1600\,\mathrm{kg}\) and \(v=30.0\,\mathrm{m/s}\): \(KE = \frac{1}{2} (1600\,\mathrm{kg}) (30.0\,\mathrm{m/s})^2\).
04

Perform the calculation

Now, let's calculate the kinetic energy: \(KE = \frac{1}{2} (1600\,\mathrm{kg}) (30.0\,\mathrm{m/s})^2 = 800\,\mathrm{kg}\cdot (900\,\mathrm{m^2/s^2}) = 720,\!000\,\mathrm{J}\).
05

State the final answer

The kinetic energy of the automobile is \(720,\!000\,\mathrm{J}\).

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Most popular questions from this chapter

(a) If the length of the Achilles tendon increases \(0.50 \mathrm{cm}\) when the force exerted on it by the muscle increases from \(3200 \mathrm{N}\) to $4800 \mathrm{N},$ what is the "spring constant" of the tendon? (b) How much work is done by the muscle in stretching the tendon \(0.50 \mathrm{cm}\) as the force increases from \(3200 \mathrm{N}\) to \(4800 \mathrm{N} ?\)
(a) If forces of magnitude \(5.0 \mathrm{N}\) applied to each end of a spring cause the spring to stretch \(3.5 \mathrm{cm}\) from its relaxed length, how far do forces of magnitude \(7.0 \mathrm{N}\) cause the same spring to stretch? (b) What is the spring constant of this spring? (c) How much work is done by the applied forces in stretching the spring \(3.5 \mathrm{cm}\) from its relaxed length?
How much work must Denise do to drag her basket of laundry of mass $5.0 \mathrm{kg}\( a distance of \)5.0 \mathrm{m}$ along a floor, if the force she exerts is a constant \(30.0 \mathrm{N}\) at an angle of \(60.0^{\circ}\) with the horizontal?
Justin moves a desk \(5.0 \mathrm{m}\) across a level floor by pushing on it with a constant horizontal force of \(340 \mathrm{N}\). (It slides for a negligibly small distance before coming to a stop when the force is removed.) Then, changing his mind, he moves it back to its starting point, again by pushing with a constant force of \(340 \mathrm{N}\). (a) What is the change in the desk's gravitational potential energy during the round-trip? (b) How much work has Justin done on the desk? (c) If the work done by Justin is not equal to the change in gravitational potential energy of the desk, then where has the energy gone?
Human feet and legs store elastic energy when walking or running. They are not nearly as efficient at doing so as kangaroo legs, but the effect is significant nonetheless. If not for the storage of elastic energy, a \(70-\mathrm{kg}\) man running at \(4 \mathrm{m} / \mathrm{s}\) would lose about \(100 \mathrm{J}\) of mechanical energy each time he sets down a foot. Some of this energy is stored as elastic energy in the Achilles tendon and in the arch of the foot; the elastic energy is then converted back into the kinetic and gravitational potential energy of the leg, reducing the expenditure of metabolic energy. If the maximum tension in the Achilles tendon when the foot is set down is \(4.7 \mathrm{kN}\) and the tendon's spring constant is $350 \mathrm{kN} / \mathrm{m},$ calculate how far the tendon stretches and how much elastic energy is stored in it.
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