Problem 4.58 A block is given an initial speed of 4.5 m/s up the 25.0 plane show

Question

Problem 4.58

A block is given an initial speed of 4.5 m/s up the 25.0 plane shown in (Figure 1) . Ignore friction.

Part A

How far up the plane will it go?

Express your answer to two significant figures and include the appropriate units.

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Part B

How much time elapses before it returns to its starting point?

Express your answer to two significant figures and include the appropriate units.

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Figure 1 of 1

Problem 4.58

A block is given an initial speed of 4.5 m/s up the 25.0 plane shown in (Figure 1) . Ignore friction.

Part A

How far up the plane will it go?

Express your answer to two significant figures and include the appropriate units.

SubmitHintsMy AnswersGive UpReview Part

Part B

How much time elapses before it returns to its starting point?

Express your answer to two significant figures and include the appropriate units.

xmaxx0 =

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t =

Figure 1 of 1

Explanation / Answer

Let:
m be the mass of the block,
g be the acceleration due to gravity,
s be the distance travelled up the slope,
u be the initial speed of the block,
a be the inclination of the plane to the horizontal,
t be the time travelling each way,
T be the total time.

(a)

The block will stop when its potential energy equals its initial kinetic energy:
mgs sin(a) = mu^2 / 2
s = u^2 / [ 2g sin(a) ]
= 4.5^2 / [ 2 * 9.81 sin(25) ]
= 2.44 m

(b)
0 = u - gt sin(a)
t = u / [ g sin(a) ]
T = 2u / [ g sin(a) ]
= 2 * 4.5 / [ 9.81 sin(25) ]
= 2.17 sec.

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