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Chapter 6: Problem 4

The bumper of a new car is being tested. The \(2300-\mathrm{kg}\) vehicle, moving at \(15 \mathrm{~m} / \mathrm{s}\), is allowed to collide with a bridge abutment, being brought to rest in a time of \(0.54 \mathrm{~s}\). Find the average force that acted on the car during impact.

Short Answer

Expert verified
The average force that acted on the car during the impact is -63894 N.

Step by step solution

01

Identify given values

The mass of the vehicle (\(m\)) is given as 2300 kg. The initial speed of the vehicle (\(v_i\)) is given as 15 m/s. The final speed of the vehicle (\(v_f\)) is 0 m/s, since it is brought to rest. The time (\(t\)) during which the car is brought to rest is given as 0.54 seconds.
02

Calculate the acceleration

The acceleration (\(a\)) can be calculated using the formula for acceleration, which is: \(a = \frac{{v_f - v_i}}{t}\). By substituting the given values into this equation, the acceleration can be calculated as \(a = \frac{{0 - 15}}{0.54} = -27.78 \, \mathrm{m/s^2}\). Negative sign indicates deceleration.
03

Calculate the force

The average force (\(F\)) that acted on the car during impact can be calculated using Newton's second law: \(F = m \cdot a\). Substituting the values of mass and acceleration into the equation, we get the force as \(F = 2300 \cdot -27.78 = -63894 \, \mathrm{N}\). The negative sign indicates that the force acted in the opposite direction to the car's initial motion.

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Most popular questions from this chapter

A \(4.88\) -kg object with a speed of \(31.4 \mathrm{~m} / \mathrm{s}\) strikes a steel plate at an angle of \(42.0^{\circ}\) and rebounds at the same speed and angle (Fig. 6-19). What is the change (magnitude and direction) of the linear momentum of the object?

In the laboratory, a particle of mass \(3.16 \mathrm{~kg}\) moving at \(15.6 \mathrm{~m} / \mathrm{s}\) to the left collides head-on with a particle of mass \(2.84 \mathrm{~kg}\) moving at \(12.2 \mathrm{~m} / \mathrm{s}\) to the right. Find the velocity of the center of mass of the system of two particles after the collision.

A \(2000-\mathrm{kg}\) truck traveling north at \(40.0 \mathrm{~km} / \mathrm{h}\) turns east and accelerates to \(50.0 \mathrm{~km} / \mathrm{h}\). What is the magnitude and direction of the change of the truck's momentum?

A \(2500-\mathrm{kg}\) unmanned space probe is moving in a straight line at a constant speed of \(300 \mathrm{~m} / \mathrm{s}\). A rocket engine on the space probe executes a burn in which a thrust of \(3000 \mathrm{~N}\) acts for \(65.0 \mathrm{~s}\). What is the change in momentum (magnitude only) of the probe if the thrust is backward, forward, or sideways? Assume that the mass of the ejected fuel is negligible compared to the mass of the space probe.

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