How Do You Calculate G-Force in a Gravity-Powered Track Simulation?

[mdawg77]

It's been a long time since I've had to think about some of these equations. Hoping for a little assistance.

I have a track which will accelerate a cart using gravity alone based on varying angles of the track. The cart will be decelerated rapidly at the end by simulating a collision.

I need to create a curve that plots angle of track vs. deceleration force/shear force/g-force on the cart.

The length of the track is roughly 2.5m
The angles will be theoretically from 0 degrees to 90 degrees (upright)
For argument sake, the mass will be 0.01
Initial velocity = 0
Final velocity after deceleration = 0

Do not know how to calculate time of deceleration
Do not know how to accurately calculate velocity at impact
Do not remember how to incorporate the angle of track into above equations (Definitely do not remember my trig...how sad...)

Help would be greatly appreciated.

Thanks

 

[physics_31415]

Can you use energy methods? When the cart is at the top of the track it has an inital potential energy (mgh). At the bottom of the track the initial potential energy (less any frictional losses) will be converted into kinetic energy. That will allow you to calculate the velocity at impact.

The time required to decelerate depends on the kinetic energy the cart has and how fast it is dissipating that energy (via friction, air resistance, etc...).