# Maximum Velocity Around a Curve

• Redrover33
In summary, the conversation discusses a motorcycle and rider traveling at a steady speed over a hill with a radius of curvature. The normal force and centripetal force experienced by the rider and motorcycle are calculated, but the maximum speed at which the motorcycle and rider would lose contact with the hill is not given due to lack of information on the frictional force and coefficient of friction. The conversation also clarifies that it is the normal force and not friction that keeps the motorcycle on its track on the hill.
Redrover33

## Homework Statement

A motorcycle (290kg) and rider (55kg) crest the top of a hill at a steady speed of 25m/s. The hill has a radius of curvature of 126m.
a) What is the magnitude of the normal force experienced by the rider?
b) What is the magnitude of the centripetal force experienced by the motorcycle?
c) At what speed would the motorcycle and rider lose contact with the surface of the hill?

## Homework Equations

Fn = m*g
A = (v^2)/r
Ff = Us*Fn

Where Fn = Normal Force, Ff = Frictional Force, Us = Max static friction

## The Attempt at a Solution

So a) and b) are no problem but its c) that has been bugging me all night. From what I can tell, there isn't enough information to find the maximum speed the rider can go. Am I wrong? I know that the centripetal acceleration x mass is = to the frictional force but we aren't given the maximum frictional force or the coefficient of friction.

No, it is not friction that keeps the motorcycle on its track on the hill. What you think of, it is a horizontal curved road.

Draw a picture with a hill and the motorcycle on top. What forces act on the motorcycle and man? Find the normal force and note that the road can only exert an upward force. If this normal force should be zero or negative to make the crest, the motorcycle loses contact with the road. ehild

## What is maximum velocity around a curve?

Maximum velocity around a curve refers to the highest speed that an object can achieve while maintaining a circular motion along the curve. It takes into account the radius of the curve, the mass of the object, and the centripetal force acting on the object.

## How is maximum velocity around a curve calculated?

The formula for calculating maximum velocity around a curve is v = √(r * μ * g), where v is the maximum velocity, r is the radius of the curve, μ is the coefficient of friction, and g is the acceleration due to gravity.

## What factors affect maximum velocity around a curve?

The factors that affect maximum velocity around a curve include the radius of the curve, the mass of the object, the coefficient of friction between the object and the surface of the curve, and the centripetal force acting on the object.

## Why is maximum velocity important in circular motion?

Maximum velocity is important in circular motion because it determines the stability and safety of the object moving along the curve. If the velocity exceeds the maximum, the object may lose control and veer off the curve.

## How can maximum velocity around a curve be increased?

The maximum velocity around a curve can be increased by increasing the radius of the curve, decreasing the mass of the object, increasing the coefficient of friction, or increasing the centripetal force acting on the object.

• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Mechanical Engineering
Replies
14
Views
1K
• Introductory Physics Homework Help
Replies
12
Views
2K
• Introductory Physics Homework Help
Replies
15
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
2K