# Calculate Force on Bike at 8.3 m/s: umg + mv^2/R

• Naeem
In summary, the biology student rides her bike around a corner with a radius of 24 meters and a speed of 8.3 m/sec. The combined mass of the student and the bike is 87 kg, with a coefficient of static friction between the bike and the road of μs = 0.39. The magnitude of the total force between the bike tire and the road can be calculated using the equation F = mv^2/R + μsmg, taking into account the normal force, weight, and friction force. This equation also shows that the centripetal force must come from friction as there is no other lateral force acting on the bike.
Naeem
Q. A biology student rides her bike around a corner of radius 24 meter at a steady speed of 8.3 m/sec. The combined mass of the student and the bike is 87 kg. The coefficent of static friction between the bike and the road is μs = 0.39.

What is the magnitude of the total force between the bike tire and the road?

Is it F = umg + mv^2 / R [ 'u' here is the static firction 0.39 ]

Is this right.

No.The friction force is centripetal force...It prevents slipping.So what are the forces involved there...?

Daniel.

Force of gravity and Normal force, what else can it be?

There must be 3:what about the friction force...?

Daniel.

Ok, I agree 3 forces,

but the final eqn,

would it be something like this:

mg + mv^2/R +Us.mg

Forces are vectors. Any addition of forces in this problem is going to involve vector sums.

Centripetal acceleration has to come from somewhere. The equation that tells you how big it must be, does not tell you what provides the force. Two of the forces in your equation are the same force.

Just write Newton's second law for radial and vertical direction...

Daniel.

ok you know that centripital force is given by F=mv^2/r right? since the bike is traveling in a horizintal circle, the centripital force has to be a lateral force towards the center of the circle. the only lateral force between the tire and the road is friction. in the vertical direction you have weight and normal force but they cancel each other out so they are irrelevant. therefore the total net force between the bike tire and road = Ff (force friction) and that has to equal centripital force, so the force F=Ff=mv^2/r

Last edited:
Felix83, it looks like the question about the force which the road exerts on the bike tire. That means it includes the normal recation (horizontal) and the reaction directed towards the center of the turn. Both forces dived between two tires, and they perpendicular to each other. You need to use the Pythagoras' theorem

## 1. What is the formula for calculating force on a bike?

The formula for calculating force on a bike is F = umg + mv2/R, where F is the total force, u is the coefficient of friction, m is the mass of the bike and rider, v is the velocity of the bike, and R is the radius of the circular path.

## 2. How do I determine the value of u in the formula?

The coefficient of friction, u, can be determined by conducting experiments or using tables that provide friction coefficients for different surfaces. It is a dimensionless value that represents the resistance between two surfaces in contact.

## 3. What is the significance of the velocity, v, in the formula?

The velocity, v, in the formula represents the speed at which the bike is traveling. It is squared in the formula because the force required to maintain a circular motion increases with the square of the velocity.

## 4. Can the formula be used to calculate force on a bike at any speed?

Yes, the formula can be used to calculate force on a bike at any speed as long as the other variables (u, m, and R) are known. However, it is important to note that the force may vary at different speeds due to factors such as air resistance and changes in surface conditions.

## 5. How can I use this formula to improve my biking performance?

By understanding the factors that contribute to the force on a bike, you can make adjustments to improve your performance. For example, reducing air resistance by changing your body position or choosing a smoother surface can decrease the force required to maintain a certain speed. Additionally, increasing your speed will also increase the force, so you can use this formula to set goals and track your progress as a cyclist.

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