An incline is angled at theta = 32 degrees. The incline is frictionless everywhe

Question

An incline is angled at theta = 32 degrees. The incline is frictionless everywhere except for a sectional of length L = 3.21m, where the coefficient of kinetic friction is 0.252. A 2.6- kg block has a initial speed of 3.43 m/s at the top of the incline, aa vertical distance of h = 5.78 m from the bottom. At the bottom of the incline, the block slides along a frictionless track until it reaches a spring with a spring constant 206 N/m. Using the law of conservation of energy, calculate how far the block compresses the spring when the block momentarily stops.

Explanation / Answer

Energy at the top of incline=1/2mv^{2}+mgh

/Applying energy conservation at when the block reaches bottom

(1/2*mv^{2}+mgh-mu mgcos heta*L=1/2mv^{2}=1/2kx^{2})

solving we get x=1.18 m

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