Centripetal acceleration acting on a parcel

[cmcd]

Homework Statement

A parcel sits on a seat angled θ to the horizontal. The car is traveling along a local radius of curvature of 80m and is traveling 20m/s at the dip. For what value of theta will the parcel not slip?

Will someone check that my force diagram is correct?
Thanks,
cmcd

http://s1372.photobucket.com/user/cmcdona22/media/001_zps29188e8a.jpg.html

 

[cmcd]

*.*.

 

[cmcd]

$$\rho_0$$

 

[cmcd]

$$\rho(h)=\rho_0\exp^-\frac{\rho_0g_ph}{p_0}$$

 

[rezeew]

I can confirm that your force diagram appears to be correct. The centripetal force, represented by the vector Fc, is directed towards the center of the circular motion, while the weight of the parcel, represented by the vector mg, is directed downwards. The angle θ represents the angle between the seat and the horizontal, and it is important to note that the centripetal force must be equal to the weight in order for the parcel to not slip. Therefore, the equation to solve for θ would be Fc = mg, which can be rearranged to θ = tan^-1(v^2/rg), where v is the velocity (20 m/s) and r is the radius of curvature (80 m). Solving this equation gives a value of approximately 9.5 degrees for θ. Therefore, if the angle between the seat and the horizontal is less than 9.5 degrees, the parcel will not slip. I hope this helps.