What is the acting net force.

Question

Michael rides a roller coast and enters the bottom of a dip with a radius of curvature of 8.0 m. At the bottom of the dip, he is traveling with a speed of 17 m/s. What is the net force acting on Michael's 65-kg body?

Answer 1

Hi Mohamed.  See my previous answer for a question of yours regarding the nature of the centripetal force.

 

At the moment Michael is at the bottom, there are two forces acting:  the normal force of his seat, upward, and the gravitational force, down.  These must result in the centripetal force, which points up.  However, we do not even need to set up Newton's second law here.  We only have to realize that, in an instantaneous moment like this, the net force on Michael, traveling in his circle, must be the centripetal force. 

 

Therefore, you only need calculate the centripetal force:  F_c = mv²/r

 

I hope this helps!  If you have any further questions not answered here or in my previous response to your other vertical circle question, please let me know.

Answer 2

We have two forces, the centripetal force pushing up toward the imaginary center of this curved section, and the force of gravity. Use the centripetal acceleration, a = v²/r. At the bottom of the ride, the acceleration is 90 degrees in direction from the speed, (i.e. straight up) which is tangent to the bottom of the curve. The net acceleration, then, is  (17²/8 - 9.8)  9.8 = g of gravity in meters/sec². Use your equation for force, f = ma, to find the net force acting on Michael. Note that I assumed that the force up is positive (+) and gravity is negative (-). With your answer note the sign and direction.