Question

A block with mass m = 16 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 5072 N/m after being compressed a distance x₁ = 0.568 m from the spring’s unstretched length. The floor is frictionless except for a rough patch a distance d = 2.8 m long. For this rough path, the coefficient of friction is μ_k = 0.48.

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 = 0.164 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:

the same

three times greater

three times less

nine times greater

nine times less

Answer 1

So it will be 9 times greater.

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