Question

Captain Science, unmasker of fuzzy thinkers and proponent of cosmic truth, drops a 35 kg bowling ball on a stiff spring from a height of 1.0 m and finds that the spring compresses 2 cm. If he drops the bowling ball from a height of 4.0 m, how much will the spring compress?

A. 8 cm

B. 1 cm

C. 16 cm

D. 2 cm

E. 4 cm

Answer 1

here,

the mass of ball , m = 35 kg

when height 1 , h1 = 1 m

compression for first time , x1 =2 cm = 0.02 m

using conservation of energy

m * g * (h1 + x1) = 0.5 * K * x1^2

35 * 9.81 * ( 1 + 0.02) = 0.5 * K * ( 0.02^2)

K = 1.75 * 10^6 N/m

when height 2 , h2 = 4 m

compression for second time be x2

using conservation of energy

m * g * (h2 + x2) = 0.5 * K * x2^2

35 * 9.81 * ( 4 + x2) = 0.5 * 1.75 * 10^6 * ( x2^2)

solving for x2

x2 = 0.04 m = 4 cm

the compression in the spring is E) 4 cm