How to Derive Formulas for Mass and Angle in Ramp Experiments?

[Asuncion]

Homework Statement

I am experimentally determining the relationship between the mass of an object and how far it slides from the bottom of a ramp? That would be my X(final) right.

I have to derive a formula between the mass of the object and how far it slides. (need help getting started-tricky) So far from what we have learned there are only three main formulas for constant-acceleration kinematics.

Secondly, I am eperimentally determining the relationship between the angle of the ramp and how far an object slides from the bottom of the ramp.

I also have to derive a formula between the angle of the ramp and how far it slides.

So far, I have beem using sin for y-component. And cos for x-component with given θ. (tricky)

Homework Equations

I also have to derive a formula between the angle of the ramp and how far it slides.

I have to derive a formula between the mass of the object and how far it slides. (need help getting started-tricky) So far from what we have learned there are only three main formulas for constant-acceleration kinematics.

The Attempt at a Solution

Familair with the three basic equations.

 

[genericusrnme]

okay, what's your problem though?
Where have you started, what do you need help with?

 

[Asuncion]

Experiment #1: Relationship between angle and how far object slides off the end of the ramp.

m = 100 kg
θ = 30°
initial starting point on ramp: 8.9 m
final starting point on ramp: -7.0m
g = 9.8 m/s2
μ= 0.3 (kinetic friction)

Now keep all the information the same except for the angle change it to 45°.

Here's the tricky part-----Come up with appropriate kinematics formula and Newton's 2nd law of motion to derive a general formula relating the angle (θ or sinθ) and the distance it slides.

Experiment #2: Relationship between the mass of an object and how far object slides off the end of the ramp.

This time keep everything the same except for the mass of the object. One object weights 10 kg., and one weighs 100 kg.

m = 100 kg
θ = 30°
initial starting point on ramp: 8.9 m
final starting point on ramp: -7.0m
g = 9.8 m/s2
μ= 0.3 (kinetic friction)

Here's the tricky part-----Come up with appropriate kinematics formula and Newton's 2nd law of motion to derive a general formula relating the object's mass (m) and the distance it slides (d).


Hummm...