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Chapter 6: Q85P (page 147)

In the early afternoon, a car is parked on a street that runs down a steep hill, at an angle of35.0°relative to the horizontal. Just then the coefficient of static friction between the tires and the street surface is 0.725. Later, after nightfall, a sleet storm hits the area, and the coefficient decreases due to both the ice and a chemical change in the road surface because of the temperature decrease. By what percentage must the coefficient decrease if the car is to be in danger of sliding down the street?

Short Answer

Expert verified

At 3.4% the coefficient decreases from the given 0.725 value of coefficient of static friction.

Step by step solution

01

Given

Original coefficient of static friction:μs=0.725

02

Understanding the concept

The problem deals with the Newton’s second law of motion which states that the acceleration of an object is dependent upon the net force acting upon the object and the mass of the object. Draw the free body diagram and then use Newton’s second law.

03

Draw the free body diagram

Free body diagram:

04

Calculate the percentage decrease in coefficient if the car is to be in danger of sliding down the street

The car is in “danger of sliding” down when,

mgsin35°=fs=fs.maxmgsin35°=μs×mgcos35°sin35°=μs×cos35°

⇒tan35°=μs⇒μs=0.700

Comparison with original value:⇒1-0.7000.725=0.034⇒3.4%less

This value represents a 3.45% decrease from the given 0.725 value of coefficient of static friction.

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Most popular questions from this chapter

Anblock of steel is at rest on a horizontal table. The coefficient of static friction between block and table is 0.52. (a) What is the magnitude of the horizontal force that will put the block on the verge of moving? (b) What is the magnitude of a force acting upward60°from the horizontal that will put the block on the verge of moving? (c) If the force acts downward at60°from the horizontal, how large can its magnitude be without causing the block to move?

A warehouse worker exerts a constant horizontal force of magnitude 85 Non a 40 kgbox that is initially at rest on the horizontal floor of the warehouse. When the box has moved a distance of 1.4 m, its speed is 1.0 m/s. What is the coefficient of kinetic friction between the box and the floor?

A student wants to determine the coefficients of static friction and kinetic friction between a box and a plank. She places the box on the plank and gradually raises one end of the plank. When the angle of inclination with the horizontal reaches30°, the box starts to slip, and it then slides 2.5 mdown the plank in 4.0 sat constant acceleration. What are

(a) the coefficient of static friction and

(b) the coefficient of kinetic friction between the box and the plank?

A roller-coaster car at an amusement park has a mass of1200kgwhen fully loaded with passengers. As the car passes over the top of a circular hill of radius18m, assume that its speed is not changing. At the top of the hill, what are the (a) magnitudeFNand (b) direction (up or down) of the normal force on the car from the track if the car’s speed isV=11m/s? What are (c)FNand (d) the direction ifV=14m/s?

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