A car moves on a level horizontal road in
a circle of radius 30.5 m. the coefficient of
friction between the tires and the road is 0.5.
The maximum speed with which the car
can round this curve without slipping is:
v = sqrt( mu * g * r)
v = sqrt( .5 * 9.8 * 30.5)
v = 12.2m/s
The correct answer is 12.2 m/s
How?
To do it you need the equation μ x m x g = (m x v^2)/R
Since we are trying to find the velocity or the maximum speed of the car we would change the equation to v^2 = μ g R
μ = 0.5 which is the friction between the tires and the road
g = gravitational acceleration (9.8 m/s^2)
r = is the radius which is 30.5 m
Once plugged into the equation it should look like this:
v^2 = (0.5 x 9.8 x 30.5)
so v^2 = 149.45
you need to square root both sides so it would be v = √(149.45)
so the answer is 12.22497444 m/s but rounded it would be 12.22 m/s
To find the maximum speed at which the car can round the curve without slipping, we need to consider the centripetal force required to keep the car on its circular path and the friction force between the tires and the road.
First, let's calculate the maximum friction force that the tires can provide. The friction force is given by the formula:
Friction force = coefficient of friction x normal force
The normal force is the force exerted by the road perpendicular to the car's tires. On a level horizontal road, this is equal to the weight of the car.
Normal force = weight = mass x gravity
Assuming the mass of the car is 1000 kg and the acceleration due to gravity is 9.8 m/s^2, we can calculate the normal force:
Normal force = 1000 kg x 9.8 m/s^2 = 9800 N
Now, let's calculate the maximum friction force:
Friction force = 0.5 x 9800 N = 4900 N
The centripetal force required to keep the car on its circular path is given by the formula:
Centripetal force = mass x velocity^2 / radius
We want to find the maximum velocity, so we can rearrange the formula to solve for velocity:
Velocity = sqrt(centripetal force x radius / mass)
Plugging in the values, we get:
Velocity = sqrt(4900 N x 30.5 m / 1000 kg) ≈ 10.65 m/s
Therefore, the maximum speed at which the car can round the curve without slipping is approximately 10.65 m/s.
F = m Acc
mu m g = m v^2/R
v^2 = mu g R