Question

The free length of the spring that is attached to the 0.3-lb slider is 3 in. If the slider is released from rest when x = 6 in., calculate its initial acceleration. Neglect friction.

Answer 1

a = 64 ft / s²

Step-by-step explanation:

The force in a spring is given by Hooke's law

F = -k x

Let's use the initial data to calculate the spring constant

k = F / x

Reduscate to the English system

x = 3 in (1foot/12 in) =0.25 foot

k = 0.3 / 0.25

k = 1.2 lb / foot

Now we can use Newton's second law

F = ma

a = F / m

a = -k x / m

m = w / g

m = 0.3 / 32 = 0.009375

x= 6 in (1foot /12 in)= 0.5 foot

a = - 1.2 0.5 / 0.009375

a = 64 ft / s²