Circular motion - Please help, I think the book's wrong?

In summary, the conversation is about a car of mass 400kg traveling over a bump of radius 10m on a track in a fun park. The question is finding the force exerted by the track on the car when it travels over the top of the hump at a speed of 6 m/s, and the minimum speed needed for the car to leave the track at the top of the hump. The equation used is F=mv^2/r and the correct answer is 2600N. However, there is also a normal force acting in the opposite direction, making the net force exerted on the car 2500N. The conversation ends with a final thank you for the assistance.
  • #1
TheKovac
24
0
Circular motion - Please help, I think the book's wrong!?

Homework Statement


A car of mass 400kg travels over a bump of radius 10m on a track in a fun park.

a) What force is exerted by the track on the car when it travels over the top of the hump at a speed of 6 m/s.

b) What is the minimum speed needed for the car to leave the track at the top of the hump?

Homework Equations


F = mv^2/t
a=V^2/r
P=2[tex]\prod[/tex]r
A=[tex]\prod[/tex]r^2

The Attempt at a Solution


a) v= 6m/s , Fnet=?
F=mv^2/r
F= (400)(6^2)/ 10
Fnet = 1440 N - WRONG!
RIGHT - 2600N

How did they get that answer? - Could someone please help with this issue.

Kindest Regards,
TheKovac
 

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  • #2
There should be a centripetal force on the car pointing into the hump. At the top of the hump, the answer you got is the centripetal force, but at the same time there is the normal force of the car pointing in the opposite direction. The net force exerted on the car by the hump should be that of the centripetal force subtracted from the normal force.
 
  • #3
Gear300 said:
There should be a centripetal force on the car pointing into the hump. At the top of the hump, the answer you got is the centripetal force, but at the same time there is the normal force of the car pointing in the opposite direction. The net force exerted on the car by the hump should be that of the centripetal force subtracted from the normal force.

Thank you very much for your answer, you really have got me thinking now.

Does that mean:

F=ma
F= 400*9.8
Fnet = 3920N
Centripital Force = 1440

=>Fnet - Fc
=> 3920 - 1440
F= 2500N

Am I correct?
 
  • #4
Seems right to me. The answer would be between 2500N and 2600N, so I'm supposing your book may have rounded or used 10 instead of 9.8 for the acceleration due to gravity.
 
  • #5
THANK YOU TO ALL WHO ASSISTED WITH MY PROBLEM!

The matter is solved, and I am very happy with all the kind hearted assistance I received.

Have a great afternoon.

Kindest Regards,
TheKovac
 

What is circular motion?

Circular motion is the movement of an object along a circular path. This type of motion is characterized by a constant radius and a continuous change in direction.

What causes circular motion?

Circular motion is caused by a centripetal force, which is directed towards the center of the circle. This force is necessary to keep an object moving in a circular path, as without it, the object would move in a straight line.

How does circular motion differ from linear motion?

Circular motion differs from linear motion in that the direction of the motion is constantly changing in circular motion, while it remains constant in linear motion. Additionally, circular motion requires a centripetal force, while linear motion does not.

What are some real-life examples of circular motion?

Some common examples of circular motion include the motion of planets around the sun, the motion of a ball in a game of basketball, and the motion of a car around a roundabout. Any object moving in a circular path is exhibiting circular motion.

How is circular motion related to Newton's Laws of Motion?

Circular motion is related to Newton's Laws of Motion, specifically the first and second laws. The first law states that an object will remain in motion in a straight line unless acted upon by an external force, which explains why a centripetal force is necessary to maintain circular motion. The second law states that the acceleration of an object is directly proportional to the net force acting on it, which is why a centripetal force is needed to continuously change the direction of an object in circular motion.

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