1)How much work is done by the spring as it accelerates the block? J 2) What is

Question

1)How much work is done by the spring as it accelerates the block? J

2)What is the speed of the block right after it leaves the spring? m/s

3)How much work is done by friction as the block crosses the rough spot? J

4)What is the speed of the block after it passes the rough spot? m/s

5)Instead, the spring is only compressed a distance x2 = 0.099 m before being released.

How far into the rough path does the block slide before coming to rest? m

6)What distance does the spring need to be compressed so that the block will just barely make it past the rough patch when released? m

7)If the spring was compressed three times farther and then the block is released, the work done on the block by the spring as it accelerates the block is:

a)the same

b)three times greater

c)three times less

d)nine times greater

e)nine times less

A block with mass m -13 kg rests on a frictionless table and is accelerated by a spring with spring constant k- 4979 N/mm after being compressed a distance x1 0.421 m from the spring's unstretched length. The floor is frictionless except for a rough patch a distance d 2.2 m long. For this rough path, the coefficient of friction is uk 0.47.

Explanation / Answer

from the given

m = 13 kg

k = 4979 N/m

x1 = 0.421 m

d = 2.2 m

muk = 0.47

(a)

workdone will be

W = (1 / 2) k x2

(b)

the speed of the block right after it leaves the spring

vmax = x1 sqrt(k / m)

(c)

work done by the frictional force is = frictional force x displacement

frictional force

f = muk N

N = m g

displacement d = 2.2 m

  

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