Question

g 4. A student with a mass of m rides a roller coaster with a loop with a radius of curvature of r. What is the minimum speed the rollercoaster can maintain and still make it all the way around the loop?

Answer 1

The question is incomplete.

The complete question is:

A student with a mass of m rides a roller coaster with a loop with a radius of curvature of r. What is the minimum speed the rollercoaster can maintain and still make it all the way around the loop? g= 9.8m/s

r=5.5 m= 55kg

Answer: 7.3m/s

Step-by-step explanation:

Centripetal force is the force acting on a body causing circular motion towards the center which allows to keep the body on track or right path. Any combination of forces in nature can cause centripetal acceleration in various systems.

Where:

V is the tangential velocity

W is the angular velocity

M is the Mass in kg

g is the gravitational force

r is the circular radius

Apply Newton's second law of motion.

The minimum speed is also known as the critical speed is the point where the tension, frictional or normal force is zero and the only thing keeping the object in circular motion is the force of gravity.

This is explained as follows:

N + mg = mw^2r

mg = mv^2/r

Therefore,the minimum speed is:

v^2 = gr

v = square root(gr)

= sqrt(9.8N/kg)(5.5m)

=(9.8N/kg)(5.5m) ^1/2

v = 7.3m/s

Answer 2

minimum speed v=
`\sqrt({Fr}/m)}`

Step-by-step explanation:

Recall the formula for centripetal force;

Centripetal force is the force that is required to keep an object moving in circular part

`F=mv^(2) /r`

where;

F=centripetal force

m=mass of object

r=radius of curvature

v= minimum speed

To find minimum speed make v the subject of formula;

v=
`\sqrt({Fr}/m)}`