Question

A 200.0-kg coaster car is in a loop on a roller coaster. the net centripetal force on the coaster car is 3750.0 n at the top of the loop. the loop is circular with a radius of 12.00 m.

Answer 1

The speed of the roller coaster at the top of the loop is 15 m/s.

Step-by-step explanation:

To find the speed of the roller coaster at the top of the loop, we can use the equation for centripetal force:

Net centripetal force = mass × centripetal acceleration

Since the only force acting on the roller coaster at the top of the loop is the net centripetal force, we can set it equal to the product of the mass and centripetal acceleration.

Net centripetal force = mass × centripetal acceleration

3750.0 N = (200.0 kg) × centripetal acceleration

Let's solve for the centripetal acceleration:

centripetal acceleration = Net centripetal force / mass

centripetal acceleration = 3750.0 N / 200.0 kg = 18.75 m/s²

Now, we can use the centripetal acceleration to find the speed of the roller coaster at the top of the loop using the formula for centripetal acceleration:

centripetal acceleration = (v²) / r

Substituting the values we know, we have:

18.75 m/s² = (v²) / 12.00 m

Let's solve for v:

v² = (18.75 m/s²) × 12.00 m

v² = 225 m²/s²

v = √225 m/s

v = 15 m/s