Finding speed of a block on a ramp/pulley

In summary, the problem involves a 20kg block sliding on a 40 degree frictionless ramp, connected to a 30kg block by a string over a pulley. The 30kg block is also connected to a spring with spring constant 250N/m. The 20kg block is pulled 20cm down the ramp and released, and the goal is to find the speed of each block when the 30kg block is again 20cm above the floor. Using the conservation of energy equation and taking into account the kinetic and potential energies of both blocks, the speed of both blocks can be determined. The assumption is made that the connecting string remains the same length during the motion.
  • #1
tkim90
7
0

Homework Statement




A 20kg block (m1) slides on a 40 degree frictionless ramp. This block is connected to a 30kg block (m2) by a string that passes over a frictionless pulley. The 30kg block is 20cm above the floor and connected to a spring of negligible mass with spring constant 250N/m. The spring is initially unstretched and connected to the floor. The 20kg block is pulled a distance of 20cm down the ramp (so that the 30kg block is 40cm above the floor) and is released from rest. Calculate the speed of each block when the 30kg block is again 20cm above the floor (spring unstretched).



Homework Equations



Usi + Ugi +KEi = Usf + Ugf + KEf

The Attempt at a Solution



I assumed that you had to use conservation of energy to find v:
Usi + Ugi +KEi = Usf + Ugf + KEf,
where Us is Spring potential, Ug is gravitational potential and KE is kinetic energy.

KE is initially zero so we have
0.5k(xi)^2 + mghi = 0.5k(xf)^2 + mghf + 0.5mv^2

xi is 0.2m, xf is 0.4m for block 2.
I worked everything out and got 10v^2 = -64...which I'm pretty sure is incorrect. Can anyone guide me to the right direction??

Thanks!
 
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  • #2
First off, why are you so sure that your answer is incorrect? Secondly, assuming that you are wrong, we need to see the details of your work and your detailed calculations. Otherwise, it will not be easy to pinpoint where you might have gone astray.
 
  • #3
Ok, this is my work:

0.5k(xf)^2 + m2ghf + 0.5m1v^2 = 0.5k(xi)^2 + m2ghi
0.5k(0.4)[tex]^{2}[/tex] + m2g(0.4) + 0.5m1v[tex]^{2}[/tex] = 0.5k(0.2)[tex]^{2}[/tex] + m2g(0.2) + 0

0.5(250)(0.4)[tex]^{2}[/tex] + (30)(9.8)(0.4) + 0.5(20)v[tex]^{2}[/tex] = 5 + 59
20 + 117.6 + 10v[tex]^{2}[/tex] = 64
10v[tex]^{2}[/tex] = -73.6

:/
 
  • #4
You forgot two things. (1) Mass m1 is also moving, so it has final kinetic energy and (2) mass m1 has an initial and final potential energy as it rises above its initial position.
 
  • #5
OK. So to find PE of m1 before and after, I need the height of m1 before and after.
I assumed that xi for m1 is 0.2m
Using trigonometry:

sin40 = [tex]\frac{hi}{0.2meters}[/tex]
hi = 0.13m
and hf = 0m
Right?
 
  • #6
Right.
 
  • #7
Does m2 have KE as well, or only m1?
 
  • #8
Yes. Any mass that is moving has KE.
 
  • #9
So that means I need vf for m1 and m2, but that gives me two variables.
How can I solve them individually?
Do they have the same speed since they are connected?

Thanks for the help by the way.
 
  • #10
Yes, they have the same speed. What would happen if they did not have the same speed? They would have non-zero relative velocity which implies that the connecting shrink is either stretched or compressed. An implicit assumption is that the connecting string maintains the same length throughout the motion.
 

Related to Finding speed of a block on a ramp/pulley

1. How do you calculate the speed of a block on a ramp?

To calculate the speed of a block on a ramp, you will need to measure the height of the ramp, the length of the ramp, and the time it takes for the block to roll down the ramp. Then, you can use the formula: speed = distance/time to determine the speed of the block.

2. What is the role of friction in finding the speed of a block on a ramp?

Friction plays a significant role in finding the speed of a block on a ramp. Friction is the force that opposes the motion of the block, and it can slow down the block's speed. When calculating the speed, it is important to consider the effects of friction and factor it into the calculations.

3. How does the angle of the ramp affect the speed of the block?

The angle of the ramp can significantly affect the speed of the block. Generally, the steeper the ramp, the faster the block will roll down due to the increased force of gravity. However, the angle can also impact the amount of friction acting on the block, which can affect the overall speed as well.

4. What is the difference between a ramp and a pulley in finding the speed of a block?

A ramp and a pulley are two different types of simple machines that can be used to find the speed of a block. The main difference is that a ramp uses the force of gravity to move the block, while a pulley uses a combination of forces, including tension and gravity. In general, a pulley can provide a more accurate measurement of speed due to its use of multiple forces.

5. What are some potential sources of error when finding the speed of a block on a ramp or pulley?

There are several potential sources of error when finding the speed of a block on a ramp or pulley. These can include inaccurate measurements of height or length, variations in the surface of the ramp or pulley, and external factors such as air resistance. It is important to minimize these sources of error and take multiple measurements to ensure accuracy.

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