3. A 2000 kg sports car moves in a horizontal circular path of 150 m\radius at a constant speed of 80 m\s.
a. magnitude of centripetal acceleration
b. magnitude of centripetal force
a. To find the magnitude of centripetal acceleration, we can use the formula:
centripetal acceleration = v^2 / r
where v is the speed of the car and r is the radius of the circular path.
Given:
v = 80 m/s
r = 150 m
Substituting the given values into the formula:
centripetal acceleration = (80 m/s)^2 / 150 m
= 6400 m^2/s^2 / 150 m
≈ 42.67 m/s^2
Therefore, the magnitude of centripetal acceleration is approximately 42.67 m/s^2.
b. To find the magnitude of centripetal force, we can use the formula:
centripetal force = mass x centripetal acceleration
Given:
mass (m) = 2000 kg (given)
centripetal acceleration = 42.67 m/s^2 (calculated in part a)
Substituting the given values into the formula:
centripetal force = 2000 kg x 42.67 m/s^2
= 85340 N
Therefore, the magnitude of centripetal force is 85340 N.