Please type the answer clearly with formulas. Thx A) The mass slides on a fricti

Question

Please type the answer clearly with formulas. Thx

A) The mass slides on a frictionless horizontal surface and then encounters a spring with a spring constant of 2000 N/m. The spring stops the sliding block. what is the maximum compression of spring?

B) Now suppose that the block and the hill have a coefficient of kinetic friction of 0.25 (the horizontal surface is a still frictionless). Now, what is the maximum compression of spring?

3. A 2.0kg block slides down a frictionless 30 degree incline from a height of h-2.0m a) The mass slides on a frictionless horizontal surface and then 309

Explanation / Answer

A) Potential energy of the block at top = kinetic energy at bottom

mgh = 0.5mv^2

v = sqrt(2gh)

= sqrt(2*9.8*2) = 6.2 m/s

This kinetic energy gets converted to spring potential energy

0.5mv^2 = 0.5kx^2

2*6.2^2 = 2000*x^2

x = 0.195 m

= 19.5 cm

B) if there is friction

Potential energy at top - energy lost due to friciton = Kinetic energy

mgh - umg cos a * d = 0.5mv^2

9.8*2 - 0.25*9.8*cos 30*(2/sin 30) = 0.5*v^2

v = 4.714 m/s

0.5mv^2 = 0.5kx^2

2*4.714^2 = 2000*x^2

x = 0.15 m

= 15 cm

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