Normal Force of Car Hitting A Bump

In summary, the normal force exerted by the seat of the car on the passenger at the top of the bump can be calculated using the formula Fn = m(v^2 / r) + mg. However, it is important to consider the direction of the forces involved, with the normal force pushing upwards and the gravity force acting downwards. The net force, which is the algebraic sum of these forces, acts downwards towards the center of the circular bump.
  • #1
Hypnos_16
153
1

Homework Statement



A car moving at 13.5 m/s encounters a bump that has a circular cross-section with a radius of 56.8 m. What is the normal force exerted by the seat of the car on a 70.8 kg passenger when the car is at the top of the bump?

v = 13.5
r = 56.8
m = 70.8kg


Homework Equations



So i know the forces acting on a object on the inside of a Loop, i know it being on the outside and hitting a bump is a factor but to me it seems like it should just be

Fn = m(v^2 / r) + mg

The Attempt at a Solution



in using that formula I've come up with
Fn = m(v^2 / r) + mg
Fn = 70.8(13.5^2 / 56.8) + (70.8 x 9.81)
Fn = 70.8(3.21) + 695
Fn = 227 + 695
Fn = 922N

but that's not the right answer,
can someone help me out?
 
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  • #2
Hypnos_16 said:

Homework Statement



A car moving at 13.5 m/s encounters a bump that has a circular cross-section with a radius of 56.8 m. What is the normal force exerted by the seat of the car on a 70.8 kg passenger when the car is at the top of the bump?

v = 13.5
r = 56.8
m = 70.8kg


Homework Equations



So i know the forces acting on a object on the inside of a Loop, i know it being on the outside and hitting a bump is a factor but to me it seems like it should just be

Fn = m(v^2 / r) + mg

[
You have a signage error. Draw a free body diagram of the passenger and identify the forces acting on the passenger including the gravity and normal forces. In which direction do these forces act? What is the direction of the net force and acceleration at the top of the bump?
 
  • #3
In a circle the acceleration is towards the middle, in the case that the man is on top of a bump wouldn't the force of gravity also be towards the middle?
meaning that that all the forces are being applied downwards?
 
  • #4
Hypnos_16 said:
In a circle the acceleration is towards the middle
yes, toward the center of the circle
in the case that the man is on top of a bump wouldn't the force of gravity also be towards the middle?
yes. again this is correct
meaning that that all the forces are being applied downwards?
Incorrect, you are missing a force. Acceleration is not a force. In addition to the gravity force, there is a contact force between the seat and the passenger, the Normal force. What is the direction of the normal force? (hint: calculate the gravity force (mg) and centripetal force (mv2/r). The centripetal force is the net force acting on the passenger).
 
  • #5
So then it's the Centripetal Force, which is the net force acting on the car, minus the gravity, since Normal Force opposes Gravity.
 
  • #6
You've got your plus and minus signs mixed up.
Per Newton 2, Fnet =ma, and since a =v2/r, then Fnet = mv2/r. Normal contact forces push toward an object. In this case , the normal force of the seat on the passenger points up (it pushes toward the passenger). Gravity forces act down. The net force, which is the algebraic sum of those 2 forces, acts down, since centripetal net forces always act in toward the center of the circle. So try that equation again. You actually have the correct magnitude of the Normal force, but you should understand in what direction it acts.
 

What is normal force?

Normal force is the perpendicular force exerted by a surface on an object that is in contact with it.

How does a car hitting a bump affect the normal force?

When a car hits a bump, the normal force between the tires and the road increases due to the impact. This increase in normal force helps to keep the car stable and prevents it from losing contact with the road.

What factors influence the normal force of a car hitting a bump?

The normal force of a car hitting a bump is influenced by the speed of the car, the size and shape of the bump, and the mass and distribution of weight in the car. The angle of the bump and the condition of the road surface can also affect the normal force.

Can the normal force of a car hitting a bump be greater than the weight of the car?

Yes, the normal force can be greater than the weight of the car when the car is accelerating or decelerating, or when it encounters a particularly large or steep bump. In these cases, the normal force helps to keep the car stable and prevents it from losing contact with the road.

What happens if the normal force of a car hitting a bump is too low?

If the normal force is too low, the car may lose contact with the road and become unstable. This can lead to loss of control and potentially result in an accident. It is important for drivers to slow down and adjust their driving to safely navigate bumps and maintain a sufficient normal force.

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