Question

PLEASE HELP!!

5. A 700 kg race car travels
around the track at 65 m/s. The track has a radius of 75 m.

a. What is the centripetal acceleration?

b. What is the centripetal force?

c. Is the net force on the car less than, equal to, or greater than the centripetal force? Why?

Answer 1

Hi there!

a.

The equation for centripetal acceleration is as follows:

`\large\boxed{a_c = (v^2)/(r)}}`

Plug in the given values to solve:

`\large\boxed{a_c = ((65)^2)/(75) = 56.33 m/s^2}`

b.

According to Newton's Second Law:

`\large\boxed{\Sigma F = ma}}`

The acceleration is v²/r, so the net force is:

`\large\boxed{\Sigma F = m((v^2)/(r))}}`

Multiply by the given mass:

`\large\boxed{\Sigma F = 700(56.33) = 39433.33 N}}`

c.

There is NO net force in the vertical direction since the object is NOT accelerating in the vertical direction (normal force and weight cancel).

Thus, the ONLY net force experienced by the object is in the horizontal direction and is EQUAL to the centripetal force.