Question

Any help with detail explanation is appreciated. Thank you!

6) Consider question 6.79 on page 199. The block is comp pring and is slowed to half of its initial speed, vi/2, wheree ressing the where v is th itial speed of the block. At half the initial speed /2, the P compress the spring is given by (sqrt is the square roo enclosed quantity) a) (sqrttk/16M)) (vi)2 b) (sqrt (M/16k)) (v) b) (sqrt (kM/16)) (vi) d) none of the above

Answer 1

6.79

a)

v_o = speed of the block = 6 m/s

k = spring constant = 500 N/m

m = mass of the block = 5 kg

x = maximum compression of the spring

Using conservation of energy

Spring energy stored in the spring = kinetic energy lost by the block

(0.5) k x² = (0.5) m v_o²

k x² = m v_o²

(500) x² = (5) (6)²

x = 0.6 m

b)

v_o = speed of the block = ?

k = spring constant = 500 N/m

m = mass of the block = 5 kg

x = maximum compression of the spring = 0.150 m

Using conservation of energy

Spring energy stored in the spring = kinetic energy lost by the block

(0.5) k x² = (0.5) m v_o²

k x² = m v_o²

(500) (0.150)² = (5) v_o²

v_o = 1.5 m/s