Banked Curve Problem: Solve Bicycle Speed & Friction Coefficient

In summary, the conversation discusses a problem involving a bicycle riding in a 20-m-radius circle on a horizontal surface. The resultant force exerted by the surface on the bicycle makes an angle of 15° with the vertical. The problem asks for the speed of the bicycle and the coefficient of static friction if the frictional force is half its maximum value. The formula for centripetal acceleration and Newton's second law are suggested as helpful hints.
  • #1
dansmith46
1
0
Hey guys I know this is probably easy for most of you but I need help with a banked curve problem. The problem is as follows "Suppose you ride a bicycle in a 20-m-radius circle on a horizontal surface. The resultant force exerted by the surface on the bicycle (normal force plus frictional force) makes an angle of 15° with the vertical. (a) What is your speed? (b) If the frictional force on the bicycle is half its maximum possible value, what is the coefficient of static friction?"
 
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  • #2
remember the formula for centripetal acceleration:

hint: ac = v2/r

where a is the centripetal acceleration, v is the velocity and r is the radius, that might get you started, and remember Newton's second law.
 

Related to Banked Curve Problem: Solve Bicycle Speed & Friction Coefficient

1. What is a banked curve problem?

A banked curve problem involves determining the speed at which a bicycle can safely travel around a curved track without slipping or skidding. It takes into account factors such as the angle of the curve, the friction coefficient of the track, and the weight of the bicycle and rider.

2. How is the speed calculated in a banked curve problem?

The speed in a banked curve problem is calculated using the formula v = √(rgtanθ), where v is the speed, r is the radius of the curve, g is the acceleration due to gravity, and θ is the angle of the curve.

3. What is the role of friction coefficient in a banked curve problem?

The friction coefficient is a measure of the amount of friction between the bicycle tires and the track surface. It is an important factor in determining the speed at which a bicycle can safely travel around a banked curve, as a higher friction coefficient allows for a higher speed without slipping or skidding.

4. How does the weight of the bicycle and rider affect a banked curve problem?

The weight of the bicycle and rider affects the forces acting on the bike, such as gravity and normal force. In a banked curve problem, a heavier bicycle and rider will require a higher speed to safely make it around the curve, as the normal force must be greater to counteract the increased gravitational force.

5. What are some real-world applications of banked curve problems?

Banked curve problems are relevant in various fields, such as transportation engineering and sports. In transportation, they are used to design safe and efficient curved roads and highways. In sports, banked curves are commonly seen in cycling and speed skating tracks, where the curved shape allows for faster speeds while maintaining stability.

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