Physics - Circular Motion?

Question

I am supposed to draw a FBD for a car traveling around a "loop-the-loop". It is at its highest point in the loop. Am I correct in saying the acceleration is straight down, towards the center? Also, was force(s) should I have on this FBD other that gravity? We are to assume negligible friction. I also need an equation for the force in the radial direction (vertical in this case). Car has mass m and loop has radius r. Should the equation be that F=m*v^2/r^2 or something similiar to that? Answer one part if that's all you can help with. Thanks!

Answer 1

FBD-free body diagram
you have the weight (mg) pointing downward and normal force pointing up (equal to weight, opposite direction), but since you know that the car has acceleration, Fnet cannot be zero and there is centripetal force pointing down, in the same direction as acceleration and F = ma= m v^2/r

Answer 2

There is a force pulling straight down on the car from gravity. There is also a second force pushing straight down on the car from the normal force from the track (the loop).

If the car is traveling in a circular loop, then it must be that the centripetal force (that is, the force that is always pointing toward the center of the loop) has a magnitude of m*v^2/r, where m is the mass of the car, r is the radius of the loop, and v is the speed of the car. If the net tug on the car was any different than that, then the car would not be traveling in a circle.

For example, imagine a satellite orbiting the earth. There is a force from gravity pulling that satellite toward the center of the earth all the time. If that satellite wants to travel in a CIRCLE of radius r, it MUST adjust its speed v so that m*v^2/r is EQUAL to the force of gravity.

In the case of the loop, if the car is FORCED to travel in a circle, then the normal force pushing against the car from the top of the loop is constantly CHANGING. This is because gravity is helping to pull toward the center of the loop at the TOP of the loop but is working AGAINST centripetal force at the BOTTOM of the loop. The NET force will always be equal to m*v^2/r though so long as the motion is truly CIRCULAR.

Answer 3

accelerates toward the center, Gravity and normal force, dont forget about the velocity

Answer 4

If the bicycle proprietor leans in, yet keeps his velocity, the centrifugal rigidity will strengthen. This definitely makes it extra handy to slip. the real reason is that if the cycle is vertical, the only rigidity against the line is the burden of the cycle and rider. by using leaning in, the bicycle proprietor directs the diverse centrifugal rigidity in the direction of the line, increasing the frictional rigidity, which enables preclude slipping.

Answer 5

What is FBD?