Practice Problems

Name____________________________________________________________

1. (ch. 5) A 9.5-kg child is hanging by one arm from monkey bars and is swinging on a vertical circle. As an approximation, assume a radial distance of 85 cm between the branch and the point where the child’s mass is located. As the child swings through the lowest point on the circle, he has a speed of 2.8 m/s. Find (a) the magnitude of the centripetal force acting on the child and (b) the magnitude of the tension in the child’s arm.

2. (ch. 5) A curve of radius 120 m is banked at an angle of 18 degrees. At what speed can it be negotiated under icy conditions where friction is negligible?

3. (ch. 5) At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis, their backs against the outer wall. At one instant the outer wall moves at a speed of 3.2 m/s, and an 83-kg person feels a 560-N force pressing against his back. What is the radius of a chamber?

4. (ch. 4) A block whose weight is 45.0 N rests on a horizontal table. A horizontal force of 36.0 N is applied to the block. The coefficients of static and kinetic friction are 0.650 and 0.420, respectively. Will the block move under the influence of the force, and, if so, what sill be the block’s acceleration? Explain your reasoning.

5. A Mercedes-Benz 300SL (m=1700 kg) is parked on a road that rises 15 degrees above the horizontal. What are the magnitudes of (a) the normal force and (b) the static frictional force that the ground exerts on the tires?

6. (ch. 4) A 60.0 kg crate rests on a level floor at a shipping dock. The coefficients of static and kinetic friction are 0.760 and 0.410, respectively. What horizontal pushing force is required to (a) just start the crate moving and (b) the static frictional force that the ground exerts on the tires?

7. (ch. 3) Two cars, A and B, are traveling in the same direction, although car A is 186 m behind car B. The speed of A is 24.4 m/s, and the speed of B is 18.6 m/s. How much time does it take for A to catch B?

8. (ch.3) A dolphin leaps out of the water at an angle of 35 degrees above the horizontal. The horizontal component of the dolphin’s velocity is 7.7 m/s. Find the magnitude of the vertical component of the velocity.

8. (ch.3) A fire hose ejects a stream of water at an angle of 35.0 degrees above the horizontal. The water leaves the nozzle with a speed of 25.0 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire?

9. (ch. 3) A jetliner is moving at a speed of 245 m/s. The vertical component of the plane’s velocity is 40.6 m/s. Determine the magnitude of the horizontal component of the plane’s velocity.

10. (ch.2) The three-toed sloth is the slowest moving land mammal. On the ground, the sloth moves at an average speed of 0.037 m/s, considerably slower than the giant tortoise, which walks at 0.076 m/s. After 12 minutes of walking, how much further would the tortoise have gone relative to the sloth?

11. A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4.0 m/s. The car is a distance d away. The bear is 26 m behind the tourist and running at 6.0 m/s. The tourist reaches the car safely. What is the maximum possible value for d?

12. (ch. 1) Two hot-air balloons are 48.2 and 61.0 m above the ground. A person in the left balloon observes that the right balloon is 13.3 degrees above the horizontal. What is the horizontal distance x between the two balloonds?

13. Two bicyclists, starting at the same place, are riding toward the same campground by two different routes. One cyclist rides 1080 m due east and then turns due north and travels another 1430 m before reaching the campground. The second cyclist starts out by heading due north for 1950 m and then turns and heads directly toward the campground. (a) At the turning point, how far is the second cyclist from the campground? (b) What direction (measured relative to due east) must the second cyclist head during the last part of the trip?