Conservation of Energy Block Velocity Problem

In summary, the problem involves a block of mass 1 kg sliding on a track with different sections, including a frictionless section AB, a section BC with a coefficient of kinetic friction of 0.25, and a frictionless section CD with a spring. The block is released from rest at point A and compresses the spring by 0.20 m. The velocity of the block at point B is 6.26 m/s, the thermal energy produced as it slides from B to C is 8.09 J, the velocity at point C is 4.80 m/s, and the stiffness constant of the spring is 576 N/m.
  • #1
Bones
108
0

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.
 
Last edited:
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  • #2
Hi Bones,

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

Bones said:

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?
 
  • #3
"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?
 
Last edited:
  • #4
Bones said:
"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!)
 
  • #5
It worked out, thanks for the help ;)
 
  • #6
Glad to help!
 

1. What is the Conservation of Energy Block Velocity Problem?

The Conservation of Energy Block Velocity Problem is a physics problem that involves calculating the final velocity of a block after it slides down a frictionless ramp. It is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed.

2. How is energy conserved in this problem?

In this problem, the initial potential energy of the block at the top of the ramp is converted into kinetic energy as it slides down. The kinetic energy is then conserved as the block reaches the bottom of the ramp and experiences no friction, resulting in no energy loss. Therefore, the total energy (potential energy + kinetic energy) remains constant throughout the problem.

3. What are the key variables involved in this problem?

The key variables in the Conservation of Energy Block Velocity Problem are the mass of the block, the height of the ramp, and the acceleration due to gravity. These variables are used to calculate the potential energy and kinetic energy of the block, which are then used to find the final velocity.

4. What is the equation used to solve this problem?

The equation used to solve the Conservation of Energy Block Velocity Problem is the Law of Conservation of Energy: PEi + KEi = PEf + KEf. This equation states that the initial potential energy (PEi) plus the initial kinetic energy (KEi) of the block must equal the final potential energy (PEf) plus the final kinetic energy (KEf) of the block.

5. How can this problem be applied in real-life situations?

The Conservation of Energy Block Velocity Problem can be applied in real-life situations, such as designing roller coasters or calculating the speed of a car going down a hill. It is also used in engineering and physics to understand the transfer and transformation of energy in various systems.

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