Understanding Energy Loss in Projectile Motion on a Ramp

[EddieV]

Homework Statement

1. Place a ramp on the table to that its bottom portion is flush with the edge of the table.
Measure the vertical height of the ramp using the table as a reference.
2. Measure the mass of the marble.
3. Use the info gathered so far to establish the initial potential energy.
4. Devise a method making use of the carbon paper and your knowledge of projectile
motion to determine the velocity that the marble leaves the ramp. Ask yourself why
you would need to know this.

Relevant Equations

Potential and Kinetic Energy Formulas
Ek = (mv^2)/2
Ep = mgh

Kinematics Equations
D = [(v1+v2)/2]T
D = v1T + 0.5v1T^2
D = v2T - 0.5v2T^2
v2^2 = v1^2 + 2aD
v2 = v1 + aT

m = mass
g = gravity
h = height
v = velocity

v1 = initial velocity
v2 = terminal velocity
a = acceleration
D = displacement
T = time

I understand the basic way of doing it if no energy was lost, but because it is and it adds this whole component of projectile motion I'm feeling a bit lost. At first I wanted to time how long it took from the top of the ramp to when it hit the ground, but I couldn't figure out a way of making it work and also thought it might be against the rules as it wants to use the carbon paper. So using the carbon paper you get to know the horizontal displacement, but I'm not sure what else. You also know the vertical displacement is the height of the table and the vertical acceleration is gravity. Hoping someone could point out a hint maybe or something I'm missing or not understanding, thank you!

 

[haruspex]

if no energy was lost, but because it is

More important than any losses due to friction is that this is rolling contact on the ramp. That will mean a specific fraction of the energy goes into rotation.

time how long it took from the top of the ramp to when it hit the ground,

That's not the useful time interval. What interval can you determine?

 

[EddieV]

Whoops, never mind I figured it out. Sorry

 

[EddieV]

The ramp is apparently curved and when the marble is shot the vertical velocity is 0 so I can solve for time of the projectile and then find initial horizontal velocity off that

 

[haruspex]

Whoops, never mind I figured it out. Sorry

Including the rotational energy?

 

[EddieV]

I found something online that showed it using that, but I didn't understand it. I have just learned about potential and kinetic energy after finishing a kinematics unit and I think we were supposed to solve it using purely that kinematics and projectile motion knowledge

 

[EddieV]

Thank you for the help though I really appreciate it

 

[haruspex]

I found something online that showed it using that, but I didn't understand it. I have just learned about potential and kinetic energy after finishing a kinematics unit and I think we were supposed to solve it using purely that kinematics and projectile motion knowledge

Ok but, when a ball rolls, 2/7 of its total KE is in the form of rotational energy. That will not contribute to its horizontal displacement when it leaves the ramp, so it will only travel √(5/7) of the distance you might have expected.