What minimum coefficient of friction between the tires and the road will allow a 3700 kg truck to navigate an unbanked curve of radius 25 m at a speed of 45 km/h?
My answer:
Fnet=ma
Ff=m(v2)/r)
Ff=(3700)(452/25)
Ff=(3700)(2025/25)
Ff=(3700)(81)
Ff=299700
Frictional force
Ff=Fnµ
299700=(3700)(9.8)µ
299700=36260µ
µ= 8.3
Is this right? Thanks for your help.
I have never heard of a friction coefficient that high. It must be wrong.
45 km/h = 12.5 m/s
You did not make the conversion to m/s. Big error there, since V gets squared.
Ff = Fn*µ = M*g*µ = M V^2/r
µ = V^2/(rg) = 0.64
Your calculations are correct up until the final step. Let's go through the steps and find the correct minimum coefficient of friction (µ).
1. Find the net force acting on the truck:
Fnet = m * (v^2 / r)
Fnet = (3700 kg) * ((45 km/h)^2 / 25 m)
Fnet = (3700 kg) * (2025 km^2/h^2 / 25 m)
Fnet = (3700 kg) * (81 km^2/h^2 / m)
Fnet = 299700 N
2. Calculate the frictional force:
Ff = Fnet
Ff = 299700 N
3. Calculate the normal force (Fn):
Fn = m * g
Fn = (3700 kg) * (9.8 m/s^2)
Fn = 36260 N
4. Determine the minimum coefficient of friction:
Ff = Fn * µ
299700 N = 36260 N * µ
µ = 299700 N / 36260 N
µ ≈ 8.26
So, the correct minimum coefficient of friction between the tires and the road that will allow the 3700 kg truck to navigate the unbanked curve is approximately 8.26.
To determine the minimum coefficient of friction required for the truck to navigate the unbanked curve, you correctly used the equation Fnet = ma. However, it seems that there was a mistake in calculating the frictional force.
The correct equation for the frictional force on a curve is Ff = mv^2/r. Substituting the given values, we have:
Ff = (3700 kg) * (45 km/h)^2 / (25 m)
Ff = (3700 kg) * [(45 x 1000 m / 3600 s)^2] / (25 m)
Ff = 3700 kg * (12.5 m/s)^2 / 25 m
Ff = 3700 kg * (156.25 m^2/s^2) / 25 m
Ff = 3700 kg * 6.25 m^2/s^2
Ff = 23125 N
Now, calculating the frictional force using the equation Ff = Fn * µ, where Fn is the normal force and µ is the coefficient of friction:
23125 N = (3700 kg) * (9.8 m/s^2) * µ
23125 N = 36260 N * µ
µ = 23125 N / 36260 N
µ ≈ 0.637
Therefore, the minimum coefficient of friction required between the tires and the road is approximately 0.637.
It seems that your calculation had some errors in the arithmetic steps, which led to an incorrect value for the coefficient of friction.