Question

Calculate the centripetal force exerted on a vehicle of mass \(m=1500 . \mathrm{kg}\) that is moving at a speed of \(15.0 \mathrm{~m} / \mathrm{s}\) around a curve of radius \(R=400 . \mathrm{m} .\) Which force plays the role of the centripetal force in this case?

Short answer

Answer: The centripetal force exerted on the vehicle is approximately 843.75 N. The force acting as the centripetal force in this case is the frictional force between the tires and the road surface.

Step-by-step solution

Recall the formula for centripetal force

The formula for centripetal force is given by: \[F_c = \frac{mv^2}{R}\] where \(F_c\) is the centripetal force, \(m\) is the mass of the object, \(v\) is its speed, and \(R\) is the radius of the circular path.

Identify the given values

We are given the following values: - Mass (\(m\)) of the vehicle = 1500 kg - Speed (\(v\)) of the vehicle = 15 m/s - Radius (\(R\)) of the circular path = 400 m

Calculate the centripetal force

Plug the given values into the formula for centripetal force: \[F_c = \frac{(1500 \, \mathrm{kg})(15.0 \, \mathrm{m/s})^2}{400 \, \mathrm{m}}\] Calculate the value of \(F_c\): \[F_c \approx 843.75 \, \mathrm{N}\]

Identify the force acting as the centripetal force

In this case, the friction between the tires of the vehicle and the road surface is what keeps the vehicle moving in a circular path. It acts toward the center of the circle (centripetal direction). So, the force acting as the centripetal force is the frictional force. The centripetal force exerted on the vehicle is approximately 843.75 N, and the force playing the role of the centripetal force in this case is the frictional force between the tires and the road surface.