Motion and force along a curved path

[a18c18]

Homework Statement

A car speeds along the curved exit ramp of a freeway. The radius of the curve is 82 m. A 76 kg passenger holds the arm rest of a car door with a 220 N force to keep from sliding across the front seat of the car. (Assume the exit ramp is not banked and ignore friction with the car seat.) What is the car's speed?

Homework Equations

v=2(3.14)r/t
u(static)=v^2/rg

The Attempt at a Solution

I tried to use the v=2(3.14)r/t formula but I don't know the time. I'm not sure what else to try.

 

[LowlyPion]

Homework Statement

A car speeds along the curved exit ramp of a freeway. The radius of the curve is 82 m. A 76 kg passenger holds the arm rest of a car door with a 220 N force to keep from sliding across the front seat of the car. (Assume the exit ramp is not banked and ignore friction with the car seat.) What is the car's speed?

Homework Equations

v=2(3.14)r/t
u(static)=v^2/rg

The Attempt at a Solution

I tried to use the v=2(3.14)r/t formula but I don't know the time. I'm not sure what else to try.

You would do better to work from the 220N force on the individual.

F=m*a since this is also equal to mV²/R you know that a = V²/R ... Calculate a. Calculate V.

 

[baba89]

I would approach this problem by first considering the forces acting on the passenger and the car. The passenger is exerting a 220 N force on the arm rest to counteract the centrifugal force acting on them due to the curved path. The car is also experiencing a centripetal force towards the center of the curve.

Using Newton's second law, we can equate these forces:

F_c = m*v^2/r

Where F_c is the centripetal force, m is the mass of the car (including the passenger), v is the speed of the car, and r is the radius of the curve.

We can then solve for v:

v = √(F_c*r/m)

Substituting in the given values:

v = √(220 N * 82 m / 76 kg)

v = √(237.9 m^2/s^2)

v = 15.4 m/s

Therefore, the car's speed is approximately 15.4 m/s.