I'm lost on this problem too! A 70kg stunt driver rounds a circular corner at 96km/hr (convert to m/s). The centripetal force on the driver is 856N. Calculate the radius in meters of the path that the driver took around the circular corner.
f = m v^2 / r ... r = m v^2 / f
do the suggested conversion to get the right units
I still don't get it where do I insert what?
v = (96000 m/hr) / (3600 m/s) = ? m/s
r = 70 kg * v^2 / 856 N
Thank you! I understand it
To solve this problem, we need to use the formula for centripetal force:
F = (m * v^2) / r
Where:
- F is the centripetal force
- m is the mass of the object in kilograms
- v is the velocity of the object in meters per second
- r is the radius of the circular path in meters
First, let's convert the velocity from kilometers per hour (km/hr) to meters per second (m/s).
To convert km/hr to m/s, divide the velocity by 3.6:
96 km/hr / 3.6 = 26.67 m/s
Next, we can rearrange the formula to solve for the radius (r):
r = (m * v^2) / F
Substituting the given values:
r = (70 kg * (26.67 m/s)^2) / 856 N
Now, let's calculate the square of the velocity:
(26.67 m/s)^2 = 711.56 m^2/s^2
Substituting this value into the formula:
r = (70 kg * 711.56 m^2/s^2) / 856 N
Now, we can calculate the radius:
r = (49709.2 kg·m^2/s^2) / 856 N
r ≈ 58.07 m
Therefore, the radius of the circular path that the driver took around the corner is approximately 58.07 meters.