Elastic Collision and Conservation of Energy

[merzperson]

SOLVED

Homework Statement

A 120g granite cube slides down a 40 degree frictionless ramp. At the bottom, just as it exits onto a horizontal table, it collides with a 225g steel cube at rest. How high above the table should the granite cube be released to give the steel cube a speed of 185cm/s?

Homework Equations

U_g=mgh
K=0.5mv²
P=mv

The Attempt at a Solution

I first calculated the momentum of the steel block (block 2):
P=mv
P₂=(.225)(1.85)
P₂=0.41625kg*m/s

Then, using conservation of momentum I deduced that the momentum of the granite block (block 1) before the collision must be equal to the momentum of the second block after the collision (P₁=0.41625kg*m/s). Using this I can find the velocity of block 1 just before the collision:
P=mv
0.41625=(0.120)v
v=3.46875m/s

Now I can find the kinetic energy of block 1 right before it hit block 2:
K=0.5mv²
K=0.5(0.120)(3.46875)²
K=0.722J

Since energy is conserved, U_g at the top of the ramp is equal to K at the bottom of the ramp (U_g=0.722J). We can now find the height of the block:
U_g=mgh
0.722=(0.120)(9.8)h
0.722=1.176h
h=0.6139m=61.39cm

Where did I go wrong?

 

[anathema]

I can see that your calculations and approach are correct. However, there may be a small error in your final answer. The height should be 61.39cm, not 61.39m. This is because the units for gravitational potential energy (Ug) are Joules, which is equivalent to kg*m2/s2. Therefore, the units for height in this equation should be meters, not centimeters. Keep up the good work!

 

[kerimek]

I would like to commend you on your thorough and well-thought-out approach to solving this problem. Your calculations and use of equations are correct, and I do not see any flaws in your methodology. However, there may be a small calculation error in your final answer. When solving for the height of the block, you should use the value for the gravitational acceleration on Earth, which is 9.81m/s2, instead of rounding it to 9.8m/s2. This may account for the slight difference in your answer compared to the given answer of 61.4cm. Overall, your understanding and application of the concepts of elastic collision and conservation of energy are sound. Keep up the good work!