/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 The \(2.5-\mathrm{Mg}\) van is t... [FREE SOLUTION] | 91影视

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Chapter 15: Problem 13

The \(2.5-\mathrm{Mg}\) van is traveling with a speed of \(100 \mathrm{~km} / \mathrm{h}\) when the brakes are applied and all four wheels lock. If the speed decreases to \(40 \mathrm{~km} / \mathrm{h}\) in \(5 \mathrm{~s}\), determine the coefficient of kinetic friction between the tires and the road.

Short Answer

Expert verified
The coefficient of kinetic friction (\( 渭 \)) between the tires and the road is calculated by using the given parameters and the principles of physics.

Step by step solution

01

Conversion of Units

First, we convert the given speeds from km/hr to m/s by multiplying with a conversion factor of \( \frac{1000 m}{3600 s} \). We get the initial speed as \( \approx 27.78 m/s \) and the final speed as \( \approx 11.11 m/s \) respectively.
02

Calculate the deceleration of the van

We can calculate the deceleration by using the formula for deceleration, which is change in speed divided by time. So, our deceleration is \( \frac{(Initial Speed - Final Speed)}{Time} \) = \( \frac{(27.78 m/s - 11.11 m/s)}{5 s} \approx 3.33 m/s^2. This value is our deceleration, which is the rate at which the van slows down.
03

Apply Newton's second law

Then, we apply Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object times its acceleration. Here we consider friction force which results in deceleration. Hence, \( F = m * a \), where m is mass and a is deceleration. Substituting the given values, the net force comes out to be \( 2.5 Mg * 3.33 m/s^2 \) kg*m/s^2 (expressed in Newton).
04

Use the friction force formula

Then, apply the law of friction which states that the friction force is equal to the coefficient of friction times the normal force. On a flat surface, the normal force is equal to the weight of the object. Hence, our equation becomes \( F = 渭 * m * g \). The force due to gravity (g) is approximately 9.81 m/s^2, and the friction force is the net force that we just calculated.
05

Solve for the coefficient of friction

Finally, we rearrange our equation from step 4 to solve for the coefficient of friction \( 渭 \). The coefficient of kinetic friction \( 渭 = \frac {F}{m*g} \) which gives the final answer.

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Most popular questions from this chapter

Sand is deposited from a chute onto a conveyor belt which is moving at \(0.5 \mathrm{~m} / \mathrm{s}\). If the sand is assumed to fall vertically onto the belt at \(A\) at the rate of \(4 \mathrm{~kg} / \mathrm{s}\), determine the belt tension \(F_{B}\) to the right of \(A\). The belt is free to move over the conveyor rollers and its tension to the left of \(A\) is \(F_{C}=400 \mathrm{~N}\)

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