2 part question, Thumbs up promised A) A block with mass m = 17 kg rests...

2 part question, Thumbs up promised

A) A block with mass m = 17 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 4112 N/m after being compressed a distance x₁ = 0.526 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 μ_k = 0.43.

How much work is done by the spring as it accelerates the block? What is the speed of the block right after it leaves the spring? How much work is done by friction as the block crosses the rough spot? What is the speed of the block after it passes the rough spot? Instead, the spring is only compressed a distance x₂ = 0.139 m before being released. How far into the rough path does the block slide before coming to rest? What distance does the spring need to be compressed so that the block will just barely make it past the rough patch when released?

B) A mass m = 12 kg rests on a frictionless table and accelerated by a spring with spring constant k = 4675 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is μ_k = 0.49. The mass leaves the spring at a speed v = 3.9 m/s.

How much work is done by the spring as it accelerates the mass? How far was the spring stretched from its unstreched length? The mass is measured to leave the rough spot with a final speed v_f = 1.6 m/s. How much work is done by friction as the mass crosses the rough spot? What is the length of the rough spot? 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? 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?

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Expert Solution

genius_generous answered 1 year ago

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