1. Velocity in Circular Motion

A car goes around a curved stretch of flat roadway of radius R = 92.0 m. The magnitudes of the horizontal and vertical components of force the car exerts on a securely seated passenger are, respectively, X = 240.0 N and Y = 600.0 N.

At what speed is the car travelling?

The correct answer needs to be 68.4 km/h. But I don't know how to get this answer, but I know to find the velocity of a particle in uniform circular motion can be found via these formulas:

$\displaystyle v=\frac{\Delta r}{\Delta t}$ and $\displaystyle v=\sqrt{a_cr}$

But I don't understand how to use the horizontal and vertical components given to obtain acceletation and displacement when mass and time are not given. Can anyone step by step show me how to solve this?

2. Originally Posted by demode
A car goes around a curved stretch of flat roadway of radius R = 92.0 m. The magnitudes of the horizontal and vertical components of force the car exerts on a securely seated passenger are, respectively, X = 240.0 N and Y = 600.0 N.

At what speed is the car travelling?

The correct answer needs to be 68.4 km/h. But I don't know how to get this answer, but I know to find the velocity of a particle in uniform circular motion can be found via these formulas:

$\displaystyle v=\frac{\Delta r}{\Delta t}$ and $\displaystyle v=\sqrt{a_cr}$

But I don't understand how to use the horizontal and vertical components given to obtain acceletation and displacement when mass and time are not given. Can anyone step by step show me how to solve this?
how do you know the circular motion is uniform?

x and y components of force indicate a set coordinate system ... is there a diagram of the situation? does the problem say where the car is w/r to the circle ... also, does it give the mass of the passenger?

3. Originally Posted by skeeter
how do you know the circular motion is uniform?

x and y components of force indicate a set coordinate system ... is there a diagram of the situation? does the problem say where the car is w/r to the circle ... also, does it give the mass of the passenger?
Here is the diagram they've given us:

No, they haven't given us the mass of the passenger and that's what confuses...

4. since the car is on a flat track, I would say that $\displaystyle x = 240 \, N$ is the horizontal centripetal force that the car exerts on the passenger and $\displaystyle y = 600 \, N$ is the vertical normal force the car exerts on the passenger ... therefore, the passenger's weight, $\displaystyle mg = 600 \, N$ , making the passenger's mass about $\displaystyle 60 \, kg$ (a reasonable figure).

note that $\displaystyle 68.4 \, km/hr = 19 \, m/s$

using the equation ...

$\displaystyle \frac{mv^2}{R} = x$

... $\displaystyle v$ will work out to the desired solution.

5. Originally Posted by skeeter
since the car is on a flat track, I would say that $\displaystyle x = 240 \, N$ is the horizontal centripetal force that the car exerts on the passenger and $\displaystyle y = 600 \, N$ is the vertical normal force the car exerts on the passenger ... therefore, the passenger's weight, $\displaystyle mg = 600 \, N$ , making the passenger's mass about $\displaystyle 60 \, kg$ (a reasonable figure).

note that $\displaystyle 68.4 \, km/hr = 19 \, m/s$

using the equation ...

$\displaystyle \frac{mv^2}{R} = x$

68.4 km/h
... $\displaystyle v$ will work out to the desired solution.
Ah, I see how you got the mass! But I still have some trouble working out $\displaystyle v$

So first I convert 92 m to 0.092 km because the final answer is in km/h.

$\displaystyle v=\sqrt{\frac{(240)(0.092)}{61.16}}=0.60 \neq 68.4 km/h$

what's the problem?

6. Originally Posted by demode
So first I convert 92 m to 0.092 km because the final answer is in km/h.
you cant do that
you need to calculate the speed in m/s and then convert to km/h

7. Originally Posted by skeeter
since the car is on a flat track, I would say that $\displaystyle x = 240 \, N$ is the horizontal centripetal force that the car exerts on the passenger and $\displaystyle y = 600 \, N$ is the vertical normal force the car exerts on the passenger ... therefore, the passenger's weight, $\displaystyle mg = 600 \, N$ , making the passenger's mass about $\displaystyle 60 \, kg$ (a reasonable figure).

note that $\displaystyle 68.4 \, km/hr = 19 \, m/s$

using the equation ...

$\displaystyle \frac{mv^2}{R} = x$

... $\displaystyle v$ will work out to the desired solution.
How did you work out $\displaystyle x = 240 \, N$?

8. Originally Posted by mathemagister
How did you work out $\displaystyle x = 240 \, N$?
it was given.

9. Originally Posted by demode
Ah, I see how you got the mass! But I still have some trouble working out $\displaystyle v$

So first I convert 92 m to 0.092 km because the final answer is in km/h.

$\displaystyle v=\sqrt{\frac{(240)(0.092)}{61.16}}=0.60 \neq 68.4 km/h$

what's the problem?
work in m/s , not km/hr. I already provided the conversion for you.