Problem

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Problem 1 Easy Difficulty

(a) What is the magnitude of the momentum of a 10,000-kg truck whose speed is 12.0 m/s? (b) What speed would a 2000-kg SUV have to attain in order to have (i) the same momentum? (ii) the same kinetic energy?

Answer

(a) $p=(10,000 \mathrm{kg})(12.0 \mathrm{m} / \mathrm{s})=1.20 \times 10^{5} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$
(b) $(\mathrm{i}) v=\frac{p}{m}=\frac{1.20 \times 10^{5} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}}{2000 \mathrm{kg}}=60.0 \mathrm{m} / \mathrm{s}$
(ii) $\frac{1}{2} m_{\mathrm{T}} v_{\mathrm{T}}^{2}=\frac{1}{2} m_{\mathrm{SUV}} v_{\mathrm{SUV}}^{2},$ so
$v_{\mathrm{SUV}}=\sqrt{\frac{m_{\mathrm{T}}}{m_{\mathrm{SUV}}}} v_{\mathrm{T}}=\sqrt{\frac{10,000 \mathrm{kg}}{2000 \mathrm{kg}}}(12.0 \mathrm{m} / \mathrm{s})=26.8 \mathrm{m} / \mathrm{s}$

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Physics 101 Mechanics

University Physics

Chapter 8

Momentum, Impulse, and Collisions

Section 1

Momentum and Impulse

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1.While waiting in his car at a stoplight, an 80-kg man and his car are suddenly accelerated to a speed of 5 m/s as the result of a rear-end collision. Assuming the time taken to be 0.3 s, find (a) the impulse on the man

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Video Transcript

problem. 8.1. We have a 10,000 kilogram truck which is moving at 12 meters per second. And the first thing we're asked about is what is the mo mentum of this? So we know that the momentum, the magnitude of the momentum is the mass times, the speed and so this works out to be 120,000 kilogram meters per second. Now be has two parts in the first part. We have a 2000 kilogram SUV and we want a momentum to be equal s So what is the speed at which this happens? But we can see from from here that PTV is going to be p over m. And this were, except to give you 60 meters per second in order to have the same momentum. Now, in the second part, we want the the kinetic energy to be equal to that of the truck. And again, we're looking for speed. So most straightforward way of doing this, of course, is take the expression for the kinetic energy for both objects and set them equals feature course, the tools her house cancel out. We find that the speed the SUV needs is going to be equal to the speed of the truck times the square root of the mass of the truck to fight it by the mass of the SUV again Just putting the numbers in. We find that this is 26.8 meters per cent of it, and it makes sense that we would want the speed to be the red. We would need the speed to be lower for the kinetic energy to be the same because this is quadratic and the speed was here. This is, you know, linear speed. So in order to get the same value, this is Speed Live to be hired at the same moment, the same kinetic energy. So our answers make sense and we're done.

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