Problem 5-2. The tips of the blades in a food blender are moving with a speed of 21 m/s in a circle that has a radius of 0.053 m. How much time does it take for the blades to make one revolution?

Problem 5-14. A child is twirling a 0.0120-kg ball on a string in a horizontal circle whose radius is 0.100 m. The ball travels once around the circle in 0.500 s. (a) Determine the centripetal force acting on the ball. (b) If the speed is doubled, does the centripetal force double? If not, by what factor does the centripetal force increase?

The speed of the ball is

The centripetal force is

(b) Since the force varies as the speed squared, when the speed is increased by a factor of 2, the force increases by a factor of

2^{2} = 4.

Problem 5-22. At what angle should a curve of radius 150 m be banked, so that cars can travel safely at 25 m/s without relying on friction?

(See fig. 5.11 in the textbook) If there is no friction, from equation (5.4), the angle is given by

Problem 5-30. Venus rotates slowly about its axis, the period being 243 days.
The mass of Venus is 4.87 × 10^{24} kg. Determine the radius for a synchronous orbit
about Venus.

Using equation (5.6)

(This is a very large orbit)

Problem 5-38. A fighter pilot dives his plane toward the ground at 230 m/s. He pulls out of the dive on a vertical circle. What is the minimum radius of the circle so that the normal force exerted on the pilot by his seat never exceeds three times his weight?

Notice that the normal force plays two roles. It provides the centripetal acceleration, but it also has to overcome gravity in the usual way. If the normal force is not to exceed 3mg, one of the mg's is his weight, so the centripetal force can be only 2mg.