A physicist rides his bike around a corner of radius 24 meters at a steady speed of 7.4 m/sec. The combined mass of the physicist and the bike is 91 kg. The coefficient of static friction between the bike and the road is μs = 0.33.
1.)If he is not skidding, what is the magnitude of the force of friction on his bike from the road?
2.)What is the magnitude of the total force between the bike tire and the road?
Mg = 91*9.8 = 892 N. = Wt. of bike with load = normal force, Fn.
1. Fs = uFn = 0.33*892 = 294 N. = Force of static friction.
1.) To find the magnitude of the force of friction on the bike from the road, we first need to understand the forces acting on the bike. Since the bike is not skidding, the force of friction between the bike tires and the road must be equal to the force of static friction.
The force of static friction can be calculated using the formula:
Fs ≤ μs * N
Where Fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.
In this case, the mass of the physicist and the bike is acting as the normal force, so we can use the formula:
N = m * g
Where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
In this case, the mass (m) is given as 91 kg. So we can calculate the normal force:
N = 91 kg * 9.8 m/s^2 = 892.8 N
Now we can substitute the values into the formula for the force of static friction:
Fs ≤ 0.33 * 892.8 N
Fs ≤ 294.024 N
Therefore, the magnitude of the force of friction on the bike from the road is approximately 294.024 N.
2.) The magnitude of the total force between the bike tire and the road can be calculated by finding the sum of all the forces acting on the bike in the radial direction.
The forces acting on the bike in the radial direction are:
1. Centripetal force: The centripetal force is the force that keeps an object moving in a circular path. It is given by the formula:
Fc = (m * v^2) / r
Where Fc is the centripetal force, m is the combined mass of the physicist and the bike, v is the velocity, and r is the radius of the corner.
Substituting the given values:
Fc = (91 kg * (7.4 m/s)^2) / 24 m
Fc = (91 kg * 54.76 m^2/s^2) / 24 m
Fc = 204.6667 N
2. Force of static friction: The force of static friction is acting opposite to the direction of movement, providing the inward force required for circular motion. We have already calculated the force of static friction to be approximately 294.024 N.
The magnitude of the total force between the bike tire and the road is the sum of these two forces:
Total force = Fc + Fs
Total force = 204.6667 N + 294.024 N
Total force = 498.69 N
Therefore, the magnitude of the total force between the bike tire and the road is approximately 498.69 N.