Question

A 4.8-kg block attached to a spring executes simple harmonic motion on a frictionless horizontal surface. At time t=0 s, the block has a displacement of -0.50m, a velocity of -0.80m/s and an acceleration of +8.3m/s2 The force constant of the spring is closest to:______.

A) 62 N/m
B) 67 N/m
C) 56 N/m
D) 73 N/m
E) 80 N/m

Answer 1

E) 80 N/m

Step-by-step explanation:

Given;

mass of the block, m = 4.8 kg

displacement of the block, x = -0.5 m

velocity of the block, v = -0.8 m/s

acceleration of the block, a = 8.3 m/s²

From Newton's second law of motion;

F = ma

Also, from Hook's law;

F = -Kx

where;

k is the force constant

Thus, ma = -kx

k = -ma/x

k = -(4.8 x 8.3) / (-0.5)

k = 79.7 N/m

k ≅ 80 N/m

Therefore, the force constant of the spring is closest to 80 N/m