How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 89 at a speed of 93 ?
Please post all physics questions with the appropriate units. 89 could be feet (unlikely), metres, and 93 could be miles per hour, km/hr, ft/sec or m/s.
In any case, the centrifugal force for an object moving at a tangential speed of v at a radius or r is
F=mv²/r
The normal reaction between the tires and the road is N = mg.
At the point of tires slipping, the coefficient of static friction is therefore:
μ = F/N
i'm not understanding the equation F=mv^2/r; what would be the m? gravity?
In SI units,
m is mass of object(kg)
v is velocity (m/s)
r is radius of circular motion (m)
F is a force in N
g is acceleration due to gravity (m s-2
μ is coefficient of static friction.
Can you now give an attempt to solve the problem?
i understood what everything else stood for, i just didn't understand how to use the given equation, F=mv^2/r, when the problem did not specify a value for m. I tried to think of another way to solve for m using the givens, but i was unsuccessful.
m in this case would be the mass of the car.
To determine the required coefficient of static friction between the tires and the road for a car to round a level curve at a given speed, we need to consider the forces acting on the car.
In this scenario, the necessary centripetal force to keep the car moving in a circular path is provided by the frictional force between the tires and the road. The equation for the centripetal force is:
Fc = (mv^2) / r
Where Fc is the centripetal force, m is the mass of the car, v is the velocity of the car, and r is the radius of the curve.
Taking into account the maximum static frictional force (Ff) that can be applied between the tires and the road, we can use the following equation:
Ff = μsN
Where Ff is the frictional force, μs is the coefficient of static friction, and N is the normal force. The normal force is equal to the weight of the car, which is given by:
N = mg
Combining these equations, we get:
Ff = μsN = μsmg
Setting the centripetal force equal to the maximum static frictional force, we can solve for μs:
Fc = Ff
(mv^2) / r = μsmg
By rearranging the equation, we find:
μs = (v^2) / (rg)
Now we can plug in the given values to calculate the coefficient of static friction:
μs = (93^2) / (89 * 9.8)
Calculating this expression, we find that the coefficient of static friction (μs) must be approximately 1.04 for the car to round the level curve of radius 89 m at a speed of 93 m/s.