Question

A 2-kg block goes around on a banked circular track at a speed of 10 m/s. There is no friction. If the track is at an angle of 20° with respect to the horizontal, what is the radius of the path? What is the centripetal force acting on the block?

Answer 1

The radius of the path is approximately 2.74 meters, and the centripetal force acting on the block is approximately 73.36 Newtons.

Step-by-step explanation:

To find the radius of the path, we can use the formula:

radius = speed² / (gravity * tan(angle))

Plugging in the values, we get:

radius = 10² / (10 * tan(20°))

Simplifying, we get:

radius = 100 / (10 * 0.364)

radius ≈ 2.74 m

To find the centripetal force, we can use the formula:

force = mass * (speed² / radius)

Plugging in the values, we get:

force = 2 * (10² / 2.74)

Simplifying, we get:

force ≈ 73.36 N