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Chapter 4: Q86. (page 107)

A coffee cup on the horizontal dashboard of a car slides forward when the driver decelerates from 45 km/h to rest in 3.5 s or less, but not if she decelerates in a longer time. What is the coefficient of static friction between the cup and the dashboard? Assume that the road and the dashboard are level (horizontal).

Short Answer

Expert verified

The coefficient of static friction between the cup and the dashboard is 0.36.

Step by step solution

01

Step 1. Variables on which the frictional force depends

The frictional force's value can be evaluated by examining the frictional coefficient between the surface and the object and the normal force acting on the object.

02

Step 2. Given information

Given data:

The initial velocity isu=45km/h.

The final velocity is t=3.5s.

The time is t=3.5s.

03

Step 3. Calculate the acceleration of the system

The acceleration of the system can be calculated as

a=v-uta=0-45km/h1000m1km1h3600s3.5sa=-3.57m/s2

Here, a negative sign indicates that the vehicle is decelerating.

04

Step 4. Calculate the coefficient of static friction

The frictional force, which balances the force acting on the coffee cup along with the motion, is

-Fr=ma-μmg=maμ=-ag

Substituting the values in the above equation,

μ=--3.57m/s29.8m/s2μ=0.36

Thus, the coefficient of static friction is 0.36.

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Most popular questions from this chapter

(II) A crate is given an initial speed of 3.0 m/s up the 25.0° plane shown in Fig. 4–60. (a) How far up the plane will it go? (b) How much time elapses before it returns to its starting point? Assumeμk=0.2.

FIGURE 4–60Crate on inclined plane. Problems 59 and 60.

A wet bar of soap slides down a ramp 9.0 m long inclined at 8.0°. How long does it take to reach the bottom? Assumeμk=0.060.

You are pushing a heavy box across a rough floor. When you are initially pushing the box, and it accelerates,

(a) you exert a force on the box, but the box does not exert a force on you.

(b) the box is so heavy that it exerts a force on you, but you do not exert a force on the box.

(c) the force you exert on the box is greater than the force of the box exerting back on you.

(d) the force you exert on the box is equal to the force of the box exerting back on you.

(e) the force that the box exerts on you is greater than the force you exert on the box.

A stone hangs by a fine thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

FIGURE 4-36 Question 9

Police investigators, examining the scene of an accident involving two cars, measure 72 m long skid marks on one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car, assuming a level road.
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