Question

1) a car of mass 999 kg traveling at 72.0 km/hour enters a flat(non-banked) and dry curve of radius 97.4 m. What is the coefficient of static friction between the tires and the road required to prevent the car from slipping ?

2) Shirin pushes a 27.1 kg crate a distance of 8.65 m along a level floor at constant velocity by pushing downward at an angle of 32.0 below the horizontal. The coefficient of kinetic friction between the crate and floor is 0.370.

a) what magnitude of force must Shirin apply to move the crate at constant velocity ?

b) how much work does Shirin do on the crate, when it is pushed this distance of 8.65 m?

3.) A soccer ball with mass 0.880 kg is initially moving with speed 1.55 m/s. Marcus Rashford kicks the ball, exerting a constant force of magnitude 97.0 N in the same direction as the ball's motion. Over what distance must Marcus's foot be in contact with the ball to increase the ball's speed to 8.33 m/s ?

Answer 1

1) car mass M = 999 kg

car speed v = 72 km/hr = 20 m/s

centrifugal force F_c = Mv²/R

The centrifugal force pushes the car away from the center. For the car to remain on track, Frictional force must be equal in magnitude. Frictional force always acts opposite to the motion

Frictional force F_f = Mg

= Mv²/R

co-efficient of friction = v²/gR = 20²/9.8*97.4 = 0.42

2) mass m = 27.1 kg,

co-efficient of friction = 0.37

frictional force F_f =mg =   0.37*27.1*9.8 = 98.26 N

force applied at 32 deg.

horizontal comp of force = FCos(32) = 0.85F

distance move s = 8.65 m

Frictional force = applied force for the box to move at const. vel.

0.85F = 98.26

a) Force to be applied F = 115.87 N

b) work done W = F_f *s = 98.26*8.65 = 850 J

Work is done against frictional force only not by the applied force, only horizontal comp. of the applied force did the work