4) What is the Length of the rough spot? 5) In a new scenario, the block only ma

Question

4) What is the Length of the rough spot? 5) In a new scenario, the block only makes it (exactly) half-way through the rough spot. How far was the spring compressed from its unstretched Length? 6) In this new scenario, what would the coefficient of friction of the rough patch need to be changed to in order for the block to just barely make it through the rough patch? 7) Return to a scenario where the blcok makes it throgh the entire rough patch. If the rough patch is tengthened to a distance of three times Longer, as the block slides through the entire distance of the rough patch, the magnitude of the work done by the force of friction is: the same three times greater three times Less nine times greater nine times Less

Explanation / Answer

1)

Here , using work energy theorum ,

work done by sping = change in kinetic energy

work done by sping = 0.5 * 12 ( 3.5^2)

work done by sping = 73.5 J

the work done by sping is 73.5 J

2)

as 0.5 kx^2 = work done by sping

0.5 * 4927 * x^2 = 73.5

x = 0.173 m

the spring is stretched 0.173 m

3)

work done by friction = change in kinetic energy

work done by friction = 0.5 * 12 *(2^2 - 3.5^2)

work done by friction = -49.5 J

the work done by friction is -49.5 J

4)

let the length is d

-d * uk * mg = W

-d * 0.42 * 12 * 9.8 = -49.5

d = 1 m

the length of rough spot is 1 m

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