When you take your 1200 kg car out for a spin, you go around a corner of radius 54.5 m with a speed of 16.2 m/s. The coefficient of static friction between the car and the road is 0.95. Assuming your car doesn't skid, what is the force exerted on it by static friction?
F(fr) = k•N =k•m•g =0.95•1200•9.8 =11172 N,
friction force = centripetal force to keep the car on road
mv^2/R =1200•(16.2)^2/54.5 =5778.5 N
Net force = 11172-5778.5 =5393.5N
To find the force exerted on the car by static friction, we can use the centripetal force equation:
Fc = mv² / r
where Fc is the centripetal force, m is the mass of the car, v is the velocity, and r is the radius of the corner.
First, let's convert the speed to m/s:
v = 16.2 m/s
Now, let's calculate the centripetal force using the given values:
Fc = (1200 kg) * (16.2 m/s)² / 54.5 m
Simplifying the equation:
Fc = (1200 kg) * (262.44 m²/s²) / 54.5 m
Fc = 62988 kg * m²/s² / 54.5 m
Now, let's calculate the force exerted on the car by static friction. The force of friction acting towards the center of the circular path is equal to the centripetal force:
Fs = Fc
Since the force of friction is equal to the product of the coefficient of friction and the normal force, we can write:
Fs = μ * N
where μ is the coefficient of static friction and N is the normal force.
Therefore, we have:
μ * N = Fc
We can now solve for N:
N = Fc / μ
Substituting the values into the equation:
N = 62988 kg * m²/s² / (0.95)
Simplifying the equation:
N = 66304.21 kg * m²/s²
Finally, the force exerted on the car by static friction is equal to the normal force:
Fs = N
Therefore, the force exerted on the car by static friction is approximately 66304.21 kg * m²/s².
To find the force exerted on the car by static friction, we need to calculate the maximum static frictional force.
The maximum static frictional force can be calculated using the formula:
Fs_max = μs * N
where μs is the coefficient of static friction and N is the normal force.
To find the normal force, we need to consider the forces acting on the car when it is going around the corner.
The forces acting on the car are:
1. Gravitational force (mg): This force is acting vertically downwards and its magnitude is given by the product of mass (m) and acceleration due to gravity (g = 9.8 m/s^2)
2. Centripetal force (Fc): This force is acting towards the center of the circular path and its magnitude is given by the formula Fc = m * (v^2 / r), where v is the velocity of the car and r is the radius of the corner.
Since the car is not skidding, the static frictional force provides the necessary centripetal force to keep the car moving in a circular path. Hence, the maximum static frictional force (Fs_max) is equal to the centripetal force (Fc).
Using the given values:
Mass of the car (m) = 1200 kg
Radius of the corner (r) = 54.5 m
Velocity of the car (v) = 16.2 m/s
Coefficient of static friction (μs) = 0.95
First, calculate the centripetal force:
Fc = m * (v^2 / r)
Fc = 1200 kg * (16.2 m/s)^2 / 54.5 m
Fc ≈ 5126.15 N
Now, calculate the maximum static frictional force:
Fs_max = μs * N
Since Fs_max = Fc, we can equate the two equations:
μs * N = Fc
We need to find N. Two forces are acting vertically on the car: the gravitational force (mg) and the normal force (N). The net vertical force is zero because the car is not accelerating vertically.
Therefore, the normal force is equal to the gravitational force:
N = mg
N = 1200 kg * 9.8 m/s^2
N ≈ 11760 N
Now we can calculate the maximum static frictional force:
Fs_max = μs * N
Fs_max = 0.95 * 11760 N
Fs_max ≈ 11,172 N
Therefore, the force exerted on the car by static friction is approximately 11,172 Newtons.