Question

A car of mass m follows a truck of mass 2m around a circular turn. both vehicles move at speed v. at what new speed vtruck will the net centripetal force acting on the truck equal the net centripetal force acting on the car still moving at the original speed v? state your answer in terms of v.

Answer 1

The new speed vtruck of the truck will be the same as the original speed v.

Step-by-step explanation:

To find the new speed of the truck, we need to equate the centripetal forces acting on both the truck and the car. The net centripetal force on an object moving in a circular path is given by the formula F = (mv^2)/r, where m is the mass of the object, v is its velocity, and r is the radius of the circular path.

Since the car is still moving at the original speed v, the net centripetal force on the car is (m * v^2)/r. To make the net centripetal force on the truck equal to this, the new speed of the truck, vtruck, can be found by rearranging the formula as follows:

(m * vtruck^2)/r = (m * v^2)/r

Cancelling out the mass and radius, we get vtruck^2 = v^2

Taking the square root of both sides, vtruck = v.

Therefore, the new speed of the truck, vtruck, will be the same as the original speed, v.