A 170-g hockey puck is given a push from the top of an icy ramp, so that its vel

Question

A 170-g hockey puck is given a push from the top of an icy ramp, so that its velocity at point A is 2.50 m/s down the ramp. After passing point B at the bottom of the ramp, it encounters a spring of spring constant k = 110 N/m that is compressed a distance xc until the puck comes momentarily to rest at point C. You may neglect friction. A y = 65 cm x=0 xC=C angle of ramp =35° point b at bottom of ramp or y=0 (a) What is the puck’s speed at point B? Remember to set up conservation of energy as a comparison between two locations, and solve SYMBOLICALLY before you plug in any numbers! (b) What is the maximum compression xc of the spring? Remember to set up conservation of energy as a comparison between two locations, and solve SYMBOLICALLY before you plug in any numbers!

Explanation / Answer

a)

h = height of point A = 0.65 Sin35 = 0.373 m

Va = speed at A = 2.50 m/s

m = mass of hockey = 0.170 kg

Vb = speed at point B at bottom

Using conservation of energy

Potential energy + KE at Top = KE at bottom

mgh + (0.5) m Va2 = (0.5) m Vb2

(9.8) (0.373) + (0.5) (2.50)2 = (0.5) Vb2

Vb = 3.6825 m/s

b)

Using conservation of energy

Kinetic energy at B = spring potential energy

(0.5) m Vb2 = (0.5) k x2

(0.17) (3.6825)2 = (110) x2

x = 0.145 m

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