**Educational Exercise on Forces and Stopping Power**1. **Compare the forces needed to bring a 950 kg car to rest from a speed of 100 km/hr, in two different ways:** (a) Use the work-energy theorem to calculate the force needed to stop the car over a distance of 120 m, which is a fairly typical distance for a non-panic stop. (b) Suppose instead the car hits a concrete barrier at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a). (c) Estimate the average power required to stop the car in case (a).**Image Explanation:**The image shows the aftermath of a car crashing into a concrete barrier. Several individuals, including emergency responders, are present at the scene. The scene depicts the severity of stopping a vehicle abruptly with a solid obstacle.

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Description: **Educational Exercise on Forces and Stopping Power**1. **Compare the forces needed to bring a 950 kg car to rest from a speed of 100 km/hr, in two different ways:** (a) Use the work-energy theorem to calculate the force needed to stop the car ove

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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**Educational Exercise on Forces and Stopping Power**

1. **Compare the forces needed to bring a 950 kg car to rest from a speed of 100 km/hr, in two different ways:**

(a) Use the work-energy theorem to calculate the force needed to stop the car over a distance of 120 m, which is a fairly typical distance for a non-panic stop.

(b) Suppose instead the car hits a concrete barrier at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).

(c) Estimate the average power required to stop the car in case (a).

**Image Explanation:**

The image shows the aftermath of a car crashing into a concrete barrier. Several individuals, including emergency responders, are present at the scene. The scene depicts the severity of stopping a vehicle abruptly with a solid obstacle.

Expert Solution

Step 1

Introduction:

It is given that-

Mass of the car m = 950 kg

Initial speed of the car v = 100 km/h = $100 km / hr \times \frac{\frac{1000 m}{1 k m}}{\frac{3600 s}{1 h r}} = 27.78 m / s$

Stopping distance in case A, d_A = 120 m

Stopping distance in case B, d_B = 2 m

It is required to determine ,The force needed in case (a), force needed in case (b), and average power in case (a).

Analysis:

As per work energy theorem, the change in kinetic energy of a body is equal to the algebraic sum of all the work-done by different forces acting on the body.

$∆ K = \sum_{} W$

In case (a), the average force is to be obtained by using the work energy theorem in a distance of 120 m gradually, whereas in case (b) the the car is stopped in a very small distance of 2 m, sharply.

In both the cases, the force should be different. In case (a) as the rate of change of momentum is gradual, the force should be less whereas in case (b), the rate is very high and hence the force must be very high in comparison to case (a).

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