A 0.600-kg block initially is pushed against a spring with k = 250.0 N/m, corres

Question

A 0.600-kg block initially is pushed against a spring with k = 250.0 N/m, corresponding it 6.00 cm. The block is released from that position, and slides without friction up the curved track. a) Initially, how much energy (in Joules) is stored in the spring? b) When the block first leaves the spring, how fast in it going? c) What maximum height in above the starting point will the block reach (before returning towards the spring)? A motor applies a constant tension of 2.50 kN to a cable passing over a pulley, putting a 520-kg crake through 6.00 m in 60.0 s up a

Explanation / Answer

here,

spring constant , K = 250 N/m

mass , m = 0.6 kg

x = 6 cm = 0.06 m

a)

the energy stored in the spring , PE = 0.5 * k * x^2

PE = 0.5 * 250 * 0.06^2 J

PE = 0.45 J

b)

let the speed of block be v

using conservation of energy

the kinetic energy gained = potential energy stored in the spring

0.45 = 0.5 * m * v^2

0.45 = 0.5 * 0.6 * v^2

v = 1.22 m/s

c)

let the maximum height be h

uisng conservation of energy

the potential energy stored in the spring initially = potential energy gained by the block

0.45 = 0.6 * 9.81 * h

h = 0.076 m = 7.6 cm

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