Block sliding down incline, hitting another block, find distance.

In summary: Physics Forum CommunityIn summary, the conversation discusses a physics problem involving two cubes on an incline and their final velocities and landing positions. The problem is solved using equations for conservation of energy and momentum, and ultimately determines the final velocities and landing positions of the cubes. The forum member is encouraged to continue with the problem and seek further help if needed.
  • #1
Tin Man
5
0

Homework Statement



In a physics lab, a cube slides down a frictionless incline as shown in the figure , and elastically strikes another cube at the bottom that is only 1/6 its mass. If the incline is 30 cm high and the table is 90 cm off the floor, where does each cube land?

Homework Equations



mgh = 1/2mu^2
mu1 + mu2 = mv1 + mv2, or...
u1 = v1 + 1/6v2
y=.5gt^2
x=vt

The Attempt at a Solution



I'm having some difficult with this problem.

u=initial velocity
v=final velocity

I first figured out the velocity, u1, of the first block using mgh=.5mu^2. I ended up with 2.42, which should be the speed at which the second block is hit.

Conservation of momentum:

m1u1 + (1/6)m2u2 = m1v1 + (1/6)m2v2

Masses cancel out, and the (1/6)m2u2 is zero, since the second block is at rest at the moment of impact from the first block. So...

u1 = v1 + (1/6)v2. Since u1 = 2.42...

2.42 = v1 + (1/6v2), or...
14.52 = 6v1 + v2

Which SHOULD mean...
v1 = 2.42 - (1/6)v2 and
v2 = 14.52-6v1.

That's where I stop. Since the definition of each velocity references itself, then I end up getting v1 = v1, and v2 = v2. That's obviously not helpful. What's the next step?

Thanks...
 
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  • #2




Thank you for bringing this problem to our attention. It seems like you have made some good progress in solving it so far. However, it appears that you are stuck at the point where you have to solve for the final velocities of both cubes. In order to do this, you will need to use the equations you have listed, specifically the equations for conservation of energy and conservation of momentum.

In this problem, you have two unknown variables (v1 and v2) and two equations (conservation of energy and conservation of momentum). This means that you can solve for both variables by setting up a system of equations and solving them simultaneously. Here's how you would do that:

1. Start by writing out the equations for conservation of energy and conservation of momentum. These are:

mgh = 1/2mu^2 (conservation of energy)
mu1 + mu2 = mv1 + mv2 (conservation of momentum)

2. Plug in the known values for mass, height, and initial velocity (m1, m2, h, and u) into the conservation of energy equation. This will give you an equation with one unknown (u1). Solve for u1.

3. Plug in the known values for mass, initial velocity, and the value you just solved for (m1, u1, and u) into the conservation of momentum equation. This will give you an equation with one unknown (v2). Solve for v2.

4. Finally, use the equation v1 = u1 - 1/6v2 to solve for v1.

By following these steps, you should be able to solve for the final velocities of both cubes and determine where they will land. If you are still having trouble, feel free to post your work and we can help you further. Good luck!


 
  • #3




Hello! It seems like you are on the right track with your calculations. However, I believe you may have made a small error in your equation for conservation of momentum. The equation should be m1u1 + (1/6)m2u2 = m1v1 + m2v2, as both masses are moving after the collision. This will give you two equations to work with and solve for v1 and v2. Additionally, you can use the equations y = 0.5gt^2 and x = vt to find the final positions of each block. I hope this helps. Keep up the good work!
 

1. How does the angle of the incline affect the distance the block will travel?

The angle of the incline will affect the distance the block travels because it determines the component of the force of gravity acting on the block in the direction of the incline. The steeper the incline, the greater the force and acceleration, resulting in a longer distance traveled.

2. What is the relationship between the mass of the blocks and the distance traveled?

The relationship between the mass of the blocks and the distance traveled depends on the coefficient of friction between the blocks and the incline. If the coefficient of friction is high, the mass of the blocks will have a greater influence on the distance traveled. However, if the coefficient of friction is low, the mass of the blocks will have a minimal effect on the distance traveled.

3. How does the velocity of the sliding block affect the distance it will travel?

The velocity of the sliding block will affect the distance it travels because it determines the initial kinetic energy of the block. The greater the initial velocity, the more kinetic energy the block has, resulting in a longer distance traveled.

4. Can the distance traveled be accurately predicted using mathematical equations?

Yes, the distance traveled can be accurately predicted using mathematical equations such as Newton's laws of motion and the equations of motion. These equations take into account factors such as mass, velocity, angle of incline, and coefficient of friction to accurately predict the distance traveled.

5. How does air resistance affect the distance the block will travel?

Air resistance can affect the distance the block travels by creating an opposing force that acts in the opposite direction of the block's motion. This can cause the block to slow down and travel a shorter distance. However, the effect of air resistance may be negligible depending on the speed and size of the blocks and the incline angle.

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