Calculating Speed of Roller Coaster Car at Top of Loop-the-Loop

In summary, the normal force equals the magnitude of the gravitational force as a roller coaster car crosses the top of a 60m diameter loop-the-loop. To find the car's speed at the top, we can use the equation Fnet = ma = mv^2/r, which gives a net force of 2mg. By setting this equal to the centripetal force and solving for v, we can find the car's speed. The net force in the y direction is zero, and the centripetal force is 2mg.
  • #1
ceday
11
0

Homework Statement


The normal force equals the magnitude of the gravitational force as a roller coaster car crosses the top of a 60m diameter loop-the-loop.



Homework Equations


What is the car's speed at the top?


The Attempt at a Solution


hello, this problem doesn't give much information
would normal force be pointing down?

so Fnet= ma=mv^2/r but its doesn't give those variables

can anyone help?
thanks :)
 
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  • #2
Don't you have all you need?

Draw a diagram.

m*g down and mv2/r up

But it says the Normal force is still m*g

If the net force must be m*g and you have m*g acting down against the centripetal force, what must the centripetal force be?
 
  • #3
Is the net force in the y direction zero?

does the centripetal force = 2mg since normal and gravity both point downward?

im lost since this coaster is upside down
 
  • #4
ceday said:
Is the net force in the y direction zero?

does the centripetal force = 2mg since normal and gravity both point downward?

im lost since this coaster is upside down

Not lost at all.

The centripetal force is 2*m*g.
 
  • #5
so would net force in the y direction = zero?

if it is zero, i don't think it would be solvable because we don't know the mass

wouldnt it be 0=mv2/r
 
  • #6
ok, i got the answer but i used the net force=2mg
i still don't understand why this is so
 
  • #7
ceday said:
ok, i got the answer but i used the net force=2mg
i still don't understand why this is so

FNormal = ∑ F = Fcentrip - Fgravity

m*g = m*v2/r - m*g

2*m*g = m*v2/r
 

1. How is the speed of a roller coaster car calculated at the top of a loop-the-loop?

The speed of a roller coaster car at the top of a loop-the-loop is calculated using the conservation of energy principle. This means that the potential energy at the top of the loop, which is determined by the car's height and mass, is equal to the kinetic energy at the bottom of the loop, which is determined by the car's velocity.

2. What factors affect the speed of a roller coaster car at the top of a loop-the-loop?

The speed of a roller coaster car at the top of a loop-the-loop is affected by the car's mass, the height of the loop, and the gravitational pull of the Earth. The shape and design of the loop can also impact the car's speed.

3. Can the speed of a roller coaster car at the top of a loop-the-loop be greater than its initial speed?

Yes, the speed of a roller coaster car at the top of a loop-the-loop can be greater than its initial speed. This is due to the car's potential energy being converted into kinetic energy as it travels through the loop.

4. How does the speed of a roller coaster car at the top of a loop-the-loop affect the ride experience?

The speed of a roller coaster car at the top of a loop-the-loop can greatly impact the ride experience. A higher speed can create a more intense and thrilling experience, while a slower speed may result in a less exciting ride.

5. Is there a maximum speed that a roller coaster car can reach at the top of a loop-the-loop?

Yes, there is a maximum speed that a roller coaster car can reach at the top of a loop-the-loop. This is determined by the car's mass, the height of the loop, and the gravitational pull of the Earth. If the car reaches a speed that is too high, it may not be able to complete the loop and could potentially derail.

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