Question

a race car rounds a curve at 52 m/s. the radius of the curve is 406 m, and the car's mass is 620 kg. (assume the car's speed remains constant. take the radially inward direction to be positive. indicate the direction with the sign of your answer.)

Answer 1

Step-by-step explanation:

To find the centripetal force acting on the car, we can use the equation for centripetal force:

F_centripetal = m * a_centripetal

where m is the mass of the car and a_centripetal is the centripetal acceleration. The centripetal acceleration can be calculated using the equation:

a_centripetal = v^2 / r

where v is the speed of the car and r is the radius of the curve.

Substituting these values, we get:

a_centripetal = (52 m/s)^2 / (406 m) = 10464 m/s^2

F_centripetal = m * a_centripetal = (620 kg) * (10464 m/s^2) = 64613120 N

The direction of the centripetal force is towards the center of the circular path, which is radially inward. Hence, the centripetal force acting on the car is:

F_centripetal = -64613120 N (the sign indicates that the force is radially inward)