a spring of force constant 200N/m is compressed through a distance of 0.05m calculate the energy stored in the string

Question

 I.calculate the energy stored in the string

II.if the energy in (I.) above is imparted to a body of mass 0.5kg to set it in motion calculate the speed acquired by the body

Answer 1

K = 200 N/m        x = .05 m

Energy stored in spring = 1/2 kx^2 = 1/2 x 200 x .05 ^2 = 0.25 J

 

m= 0.5 kg

 

PE stored in spring = KE imparted to object

0.25 J = 1/2 x 0.5 kg x v^2            v = sqrt 1 = 1 m/s

Answer 2

We use the formulas

 

F = kx            and        W = Fd

 

where:

F = Force

k = spring constant

x = distance

d = distance

W = energy

 

 

W = Fd

    = (kx)(d)

    = (200 N/m)(0.5 m)(0.5 m)

    = 0.5 Nm

 

The energy in the spring is 0.5 Nm.

 

 

Part II.

 

Since we have velocity, we can use the formula for kinetic energy.

 

KE = (1/2)mv²

 

where:

KE = W

m = mass

v = speed

 

0.5 = (1/2)(0.5)v²

 

0.5 = 0.25v²

 

2 = v²

 

√(2) = v

 

1.414 = v

 

The speed is 1.141 m/s.