Question

A large fake cookie sliding on a horizontal surface is attached to one end of a horizontal spring with spring constant k = 375 N/m; the other end of the spring is fixed in place. The cookie has a kinetic energy of 20.0 J as it passes through the position where the spring is unstretched. As the cookie slides, a frictional force of magnitude 10.0 N acts on it.

(a) How far will the cookie slide from the position where the spring is unstretched before coming momentarily to rest?
m

(b) What will be the kinetic energy of the cookie as it slides back through the position where the spring is unstretched?
J(a) How far will the cookie slide from the position where the spring is unstretched before coming momentarily to rest?
m

(b) What will be the kinetic energy of the cookie as it slides back through the position where the spring is unstretched?
J

Answer 1

a)
`x=0.301\ m`

b)
`KE=26.338\ J`

Step-by-step explanation:

Given:

• spring constant,
  `k=375\ N.m^(-1)`

• kinetic energy of cookie,
  `KE=20\ J`

• frictional force on the cookie,
  `f=10\ N`

a)

Now the kinetic energy here is changing into frictional energy and the spring potential energy.

So, by the law of energy conservation:

`KE=\rm spring\ potential\ energy+frictional\ loss`

`KE=(1)/(2) k.x^2+f.x`

where:

`x=` distance travelled by the cookie from the unstretched position to the stretched position of the spring.

`20=(1)/(2) * 375* x^2+10* x`

`375* x^2+20* x-40=0`

`x=0.301\ m`( neglecting the negative value)

b)

Now, after the compression of the spring there is no kinetic energy for the moment as the velocity of the cookie is zero but there is a spring potential energy due to the compressed spring.

So, here we have the spring potential energy getting converted into kinetic energy and the frictional losses:

`U=KE+E_f`

where:

U = spring potential energy

KE = kinetic energy

`E_f=` energy lost due to friction

`(1)/(2) * 375* 0.301=KE+10* 0.301`

`KE=26.338\ J`