a 47 kg person in a rollercoaster moving through the bottom of a curved track of radius 47.7 m feels a normal force of 895 N. What is the net centripedal force acting on the person.
I still couldn’t solve it sorry
the normal force is the reaction to the person's weight ... m * g
... PLUS ... the centripetal force
centripetal = normal - weight
No problem! I can help you with that. To find the net centripetal force acting on the person, we need to start by understanding the forces acting on the person in the rollercoaster.
In this case, the normal force (N) is acting vertically upwards, and the weight (mg) is acting vertically downwards. The net centripetal force (Fc) is acting towards the center of the curved track, perpendicular to the weight and normal force.
Since the person is not sinking into the rollercoaster or flying off, the normal force and weight must be balanced. Therefore, we can write the equation:
N + mg = 0
We know the normal force (N) is 895 N, and the weight (mg) can be calculated using the person's mass (47 kg) and the acceleration due to gravity (9.8 m/s^2):
mg = (47 kg)(9.8 m/s^2) = 461.6 N
Now we can substitute the values into the equation:
895 N + 461.6 N = 0
Simplifying,
1356.6 N = 0
This equation doesn't hold true, which means there must be an additional force acting on the person. This additional force is the net centripetal force (Fc), which is the force that keeps the person moving in a circular path.
To find the net centripetal force, we need to rearrange the equation:
Fc = N + mg
Plugging in the known values,
Fc = 895 N + 461.6 N
Fc = 1356.6 N
Therefore, the net centripetal force acting on the person is 1356.6 N.
No problem! I'll walk you through the steps to solve the problem.
To find the net centripetal force acting on the person, we need to use the equation:
Net Centripetal Force = (Normal Force - Weight)
The weight of the person can be found using the formula:
Weight = mass × acceleration due to gravity
1. Calculate the weight of the person:
Weight = mass × acceleration due to gravity
Weight = 47 kg × 9.8 m/s²
2. Calculate the net centripetal force:
Net Centripetal Force = (Normal Force - Weight)
Given that the normal force is 895 N, substitute the values in the equation:
Net Centripetal Force = (895 N - Weight)
Now you can substitute the calculated weight value into the equation to find the net centripetal force.