How Is the Force on a Child in a Roller Coaster Calculated?

[Austin Gibson]

Homework Statement

:[/B]
A child of mass 40.0 kg is in a roller coaster car that travels in a loop of radius 7.30 m. At point A the speed of the car is 15.0 m/s, and at point B, the speed is 15.6 m/s. Assume the child is not holding on and does not wear a seat belt.

What is the force (in N) of the car seat on the child at point B? (Enter the magnitude.)

Homework Equations

Fc = [(mv^2)/r]
Fc = ma

The Attempt at a Solution

:

I solved (a) and (c).
I solved (a) by inserting the mass, speed, and radius into the equation [(mv^2)/r] and subtracting by (mass*gravity).
My equation for (b) was [(mv^2)/r * cos30] - mg = [(40*(15.6^2)/7.3*cos30) - (40*9.8) = 762.8 N. That was incorrect. What's improper about my equation? [/B]

 

[SammyS]

Homework Statement

:[/B]
A child of mass 40.0 kg is in a roller coaster car that travels in a loop of radius 7.30 m. At point A the speed of the car is 15.0 m/s, and at point B, the speed is 15.6 m/s. Assume the child is not holding on and does not wear a seat belt.

What is the force (in N) of the car seat on the child at point B? (Enter the magnitude.)

View attachment 232155

Homework Equations

Fc = [(mv^2)/r]
Fc = ma

The Attempt at a Solution

:[/B]

I solved (a) and (c).
I solved (a) by inserting the mass, speed, and radius into the equation [(mv^2)/r] and subtracting by (mass*gravity).
My equation for (b) was [(mv^2)/r * cos30] - mg = [(40*(15.6^2)/7.3*cos30) - (40*9.8) = 762.8 N. That was incorrect. What's improper about my equation? [/B]

In what direction is the centripetal force at point B ?

Also, is there any net force on the child at point B ?

 

[Austin Gibson]

In what direction is the centripetal force at point B ?

120 degrees(90+30)?

 

[Austin Gibson]

I solved it by applying (cos 30) to mg instead of the centripetal force.