Brake or turn? The figure depicts an overhead view of a car's path as the car travels toward a wall. Assume that the driver begins to brake the car when the distance to the wall is d = 109 m, and take the car's mass as m = 1410 kg, its initial speed as vo = 38.0 m/s, and the coefficient of static friction as μ = 0.530. Assume that the car's weight is distributed evenly on the four wheels, even during braking. (a) What magnitude of frictional force is needed (between tires and road) to stop the car just as it reaches the wall? (b) What is the maximum possible static friction fs, max? (c) If the coefficient of kinetic friction between the (sliding) tires and the road is Uk = 0.440, at what speed will the car hit the wall? To avoid the crash, a driver could elect to turn the car so that it just barely misses the wall, as shown in the figure. (d) What magnitude of frictional force would be required to keep the car in a circular path of radius d and at the given speed vo? (a) Number i (b) Number i (c) Number i (d) Number i Units Units Units Units Car path Wall

A block with mass m starting from rest at point A is sliding down a rough incline with kinetic coefficient of friction µ. The incline has angle 0 with respect to the horizontal sur- face. As the block slides down for a distance O 1. KB = m gs cos 0 – µ mgs cos 0 8, it passes point B. O 2. KB = mgs sin 0 + µ m gs sin 0 O 3. KB = mgs cos0 – µm gs sin 0 m O 4. KB = mgs sin 0 + µ mgs cos 0 v =0 O 5. KB = mgs sin 0 – µm g s sin 0 m О6. Кв — тgs sin@ — дтдs cos® B O 7. KB = m gs cos 0 + µ mgs cos 0 O 8. KB = m gs cos 0 + µ mgs sin 0 Find the kinetic energy of the block as it passes B.

A constant applied force ?p of 15.0 N pushes a box with a mass ?=7.00 kg a distance x=15.0 m across a level floor. The coefficient of kinetic friction between the box and the floor is 0.150. Assuming that the box starts from rest, what is the final velocity ?f of the box at the 15.0 m point? If there were no friction between the box and the floor, what applied force Fnew would give the box the same final velocity?

You are pushing a rubber crate against a concrete floor. The two surfaces have a static coefficient of friction of 0.61 and a kinetic coefficient of friction of 0.49. The floor is horizontal, and the crate has a mass of 25.0 kg, and is initially at rest. You are pushing with a horizontal force of 100 N. What is the magnitude of the force of friction in this case? Give your answer in units of N, to three significant figures.