Question

A mass resting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. It takes 3.6 J of work to compress the spring by 0.13 m. If the spring is compressed, and the mass is released from rest, it experiences a maximum acceleration of Find the value of (a) the spring constant and (b) the mass.

Answer 1

(a) The spring constant is 426N/m

(b) The mass is 5.65kg

Step-by-step explanation:

(a) Energy stored in the spring (E) = 3.6J, extension (e) = 0.13m

E = 1/2Ke^2

3.6 = 1/2 × K × 0.13^2

K (spring constant) = 3.6×2/0.0169 = 426N/m

(b) F = Ke = 426 × 0.13 = 55.38N

Assuming the maximum acceleration (a) is 9.8m/s^2

Mass (m) = F/a = 55.38/9.8 = 5.65kg