The 1.5 kg physics book in figure is connected by a string to a 250 g coffee cup

Question

The 1.5 kg physics book in figure is connected by a string to a 250 g coffee cup. The book is given a push up the slope and released with a speed of 3.3 m/s . The coefficients of friction are s =0.50and k =0.20.
(Figure 1)

Part A

How far does the book slide?

Express your answer with the appropriate units.

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Part B

At the highest point, does the book stick to the slope, or does it slide back down?

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Figure 1 of 1

The 1.5 kg physics book in figure is connected by a string to a 250 g coffee cup. The book is given a push up the slope and released with a speed of 3.3 m/s . The coefficients of friction are s =0.50and k =0.20.
(Figure 1)

Part A

How far does the book slide?

Express your answer with the appropriate units.

SubmitMy AnswersGive Up

Part B

At the highest point, does the book stick to the slope, or does it slide back down?

At the highest point, does the book stick to the slope, or does it slide back down? stick to the slope slide back downhill

SubmitMy AnswersGive Up

Provide FeedbackContinue

Figure 1 of 1

20°

Explanation / Answer

Part A:

initial velocity of book=3.3m/s

mass of cup=250gm=0.25kg

mass of book=1.5kg

slope of incline=20o

Let tension in string be T and acceleration of system be a

0.25*9.8 -T=0.25a

Or, 2.45-T=0.25a...(i)

T-0.2*1.5*9.8cos20+1.5*9.8sin20=1.5a

Or, T-2.76+5.03 = 1.5a

Or, T+2.27=1.5a...(ii)

Solving (i) and (ii) ,we get

a=2.7 m/s2 (downwards along the slope)

initila velocity of book=3.3m/s(upwards along the slope)

The distance travelled by book up along the incline,before coming to rest = 3.32/(2*2.7)=2.017 m

part B:

For the book to be able to slide down from the highest position,the weight of the cup and the component of the weight of book along the slope should be more than static friction force on book

weight of cup=0.25*9.8=2.45N

Weight of book along slope=1.5*9.8*sin20=5.03N

Static fricition force on book = 0.5*1.5*9.8*cos20=6.91 N

5.03+2.45=7.48 N>6.91N

Therefore ,the book will slide back downhill

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