A car drives around a curve with radius 430 m at a speed of 32 m/s. The road is not banked. The mass of the ca?A car drives around a curve with radius 430 m at a speed of 32 m/s. The road is not banked. The mass of the car is 1400 kg. (a) What is the frictional force on the car? (b) Does the frictional force necessarily have magnitude μsN? yes or no? please expain | |
Forces acting on the car:
Earth's gravity (m*g): downward
Normal force (N): upward
Static friction (F): inward
Vertical force balance, about which we don't care:
N = m*g
Horizontal Newton's 2nd law:
F = m*a
Acceleration is centripetal acceleration, and is thus:
a = v^2/r
Thus:
F = m*v^2/r
Data:
m:=1400 kg; r:=430 m; v:=32 m/s;
Results:
A: static friction force: F = 3334 Newtons
B: No. If it did, this car would be taking the curve at a dangerous speed, because any slight disturbance could cause it to skid.
mu_s*N is the UPPER LIMIT of the static friction force, not necessarily equal to the static friction force. Remember: static friction (traction) is a force of constraint.
Only kinetic friction when present is always equal to mu_k*N.
