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...).

 

[charng]

Hello,

I am happy to help you with your G-force question. First, I would suggest reviewing the equations for calculating acceleration, velocity, and time. These equations are essential for understanding the relationship between the angle of the track and deceleration force.

To calculate the time of deceleration, you will need to use the equation t = (v-u)/a, where t is time, v is final velocity, u is initial velocity, and a is acceleration. In this case, v and u are both 0, so the equation simplifies to t = 0/a = 0. This means that the deceleration will happen instantaneously.

To accurately calculate the velocity at impact, you will need to use the equation v^2 = u^2 + 2as, where v is final velocity, u is initial velocity, a is acceleration, and s is distance. In this case, u is 0, a is the deceleration force, and s is the length of the track (2.5m). This will give you the velocity at impact.

To incorporate the angle of the track into the equations, you will need to use trigonometry. The angle of the track will determine the component of gravity that is acting on the cart. You can use the equation F = mg sinθ, where F is the force, m is the mass, g is the acceleration due to gravity, and θ is the angle of the track. This will give you the deceleration force at each angle.

I hope this helps you with your calculations. If you need further assistance, please don't hesitate to ask. Remember to always double check your equations and units to ensure accuracy. Good luck with your project!