Conservation of Energy Block Velocity Problem

[Bones]

Homework Statement

Consider the track shown in the figure. The section AB is one quadrant of a circle of radius r = 2.0 m and is frictionless. B to C is a horizontal span 3.3 m long with a coefficient of kinetic friction µk = 0.25. The section CD under the spring is frictionless. A block of mass 1 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m.

a)Determine the velocity of the block at point B.
b)Determine the thermal energy produced as the block slides from B to C.
c)Determine the velocity of the block at point C.
d)Determine the stiffness constant k for the spring.

Homework Equations

The Attempt at a Solution

I have been trying to solve this all night and have gotten this far:

a) V=square root of 2(9.8m/s^2)(2m) V=6.26m/s
b) (.25)(9.8m/s^2)(3.3m)(1kg)=8.09 J
c) 1/2(1kg)V^2-1/2(1kg)(6.26m/s)^2=-8.09J V=4.80m/s
d) -1/2(1kg)(4.80m/s)^2=1/2(-k)5.5m k=4.19N/m

Are any of these correct?

Please help me figure this out, it is due by the end of the day Thursday 10/16.

 

[alphysicist]

Hi Bones,

If possible, it would probably be good to upload an image for this problem somewhere to make sure there is no misunderstanding.

Homework Statement

Consider the track shown in the figure. The section AB is one quadrant of a circle of radius r = 2.0 m and is frictionless. B to C is a horizontal span 3.3 m long with a coefficient of kinetic friction µk = 0.25. The section CD under the spring is frictionless. A block of mass 1 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m.

a)Determine the velocity of the block at point B.
b)Determine the thermal energy produced as the block slides from B to C.
c)Determine the velocity of the block at point C.
d)Determine the stiffness constant k for the spring.

Homework Equations

The Attempt at a Solution

I have been trying to solve this all night and have gotten this far:

a) V=square root of 2(9.8m/s^2)(2m) V=6.26m/s
b) (.25)(9.8m/s^2)(3.3m)(1kg)=8.09 J
c) 1/2(1kg)V^2-1/2(1kg)(6.26m/s)^2=-8.09J V=4.80m/s
d) -1/2(1kg)(4.80m/s)^2=1/2(-k)5.5m k=4.19N/m

I don't think the right side of this equation is correct. What is the formula for the potential energy stored in a spring? And isn't the spring only compressed by 0.2m?

 

[Bones]

"At the spring, use the velocity to find it's kinetic energy again. Energy and work interchange, and the work to compress a spring is 1/2*Spring constant*Compression distance^2"

-1/2(1kg)(4.80m/s)^2=1/2(-k)(0.2m)^2 k=576N/m

Is this better?

 

[alphysicist]

"At the spring, use the velocity to find it's kinetic energy again. Energy and work interchange, and the work to compress a spring is 1/2*Spring constant*Compression distance^2"

-1/2(1kg)(4.80m/s)^2=1/2(-k)(0.2m)^2 k=576N/m

Is this better?

Yes, that looks better. (And I hope I am visualizing this correctly!)

 

[Bones]

It worked out, thanks for the help ;)

 

[alphysicist]

Glad to help!