1. Advanced Problems 2 These problems will contain:
Basic concepts of force and motion.
Usage of Newton’s laws of motion.
The concept of net force in multiple directions.

2. 1. A fire helicopter carries a 620-kg bucket of water at the end of a cable 20.0m long. As the aircraft flies back from a fire at a constant speed of 40.0m/s, the cable makes an angle of 40° with respect to the vertical.
Determine the force of air resistance on the bucket.
After filling the bucket with sea water, the pilot returns to the fire at the same speed with the bucket now making an angle of 7.00° with the vertical. What is the mass of the water in the bucket?

3. 2. A block is given an initial velocity of 5
2. A block is given an initial velocity of 5.00m/s up a frictionless 20.0° incline. How far up the incline does the block slide before coming to rest?

4. 3. Two masses are connected by a light string that passes over a frictionless pulley, as shown in the figure. If the incline is frictionless and if m1=2.00kg, m2=6kg, and θ=55°, find:
the acceleration of the masses.
the tension of the string.
the speed of each mass 2.0s after being released from rest. m2 m1 θ

5. 4. A 72. 0kg man stands on a spring scale in the elevator
4. A 72.0kg man stands on a spring scale in the elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.20m/s in 0.800s. It travels with this constant speed for the next 5.0s. The elevator then undergoes a uniform acceleration in the negative y direction for 1.50s and comes to rest. What does the spring scale register:
before the elevator starts to move?
during the first 0.8s?
while the elevator is traveling at constant speed?
during the time it is slowing down?

6. 5. A racing car accelerates uniformly from 0 to 80. 0km/h in 8. 0s
5. A racing car accelerates uniformly from 0 to 80.0km/h in 8.0s. The external force that accelerates the car is the frictional force between the tires and the road. If the tires do not slip, determine the minimum coefficient of friction between the tires and the road.

7. 6. A 3. 0kg block starts from rest at the top of a 30
6. A 3.0kg block starts from rest at the top of a 30.0° incline and slides a distance of 2.0m down the incline in 1.50s. Find:
The magnitude of the acceleration of the block.
The coefficient of friction between block and plane.
The frictional force acting on the block.
The speed of the block after it has slid 2.0m.

8. 7. To determine the coefficients of friction between rubber and various surfaces, a student uses a rubber eraser and an incline. In one experiment, the eraser begins to slip down the incline when the angle of inclination is 36.0° and then moves down the incline with constant speed when the angle is reduced to 30.0°. From these data, determine the coefficients of static and kinetic friction for this experiment.

9. 8. A block of mass 3.0kg is pushed up against a wall by a force P that makes a 50.0° angle with the horizontal as shown in the figure. The coefficient of static friction between the block and the wall is Determine the possible values for the magnitude of P that allow the block to remain stationary.
50.0° P

10. the tension in each section of rope, T1, T2, T3,T4,T5.
9. A mass M is held in place by an applied force F and a pulley system as shown in the figure. The pulleys are massless and frictionless . Find:
the tension in each section of rope, T1, T2, T3,T4,T5.
the magnitude of F.
(Hint: draw a free-body diagram for each pulley.) T4 T1 T2 T3 F T5 M

11. the magnitude of the acceleration of each block.
10. Two blocks of mass 3.50kg and 8.00kg are connected by a string of negligible mass that passes over a frictionless pulley. The inclines are frictionless. Find:
the magnitude of the acceleration of each block.
the tension in the string.
8.00kg
3.50kg
35.0°
35.0°

12. Determine the tension in the wire.
11. Consider a conical pendulum with an 80kg bob on a 10m wire making an angle of θ = 5° with the vertical.
Determine the tension in the wire.
Determine the tangential velocity of the bob. θ

13. 12. A person stands on a scale in an elevator
12. A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591N. As the elevator stops, the scale reading is 391N. Assume the magnitude of the acceleration is the same during starting and stopping, and determine …
The weight of the person.
The acceleration of the elevator.

14. 13. A 50kg parachutist jumps from an airplane and falls with a drag force proportional to the square of the speed, R=Cv2. Take C= 0.2kg/m with the parachute closed and C = 20kg/m with the parachute open.
Determine the terminal speed of the jumper both before and after the chute is open.
Write speed and position functions of time for the jumper if the original altitude of the jump is 1000 m and he is in free fall for 10s before the parachute opens.

15. 14. Suppose the boxcar below is moving with constant acceleration (a) up a hill that makes an angle (Φ) with the horizontal. If the hanging pendulum makes a constant angle (θ) with the perpendicular to the ceiling, what is a? a θ Φ

16. 15. A string under a tension of 50N is used to whirl a rock in a horizontal circle of 2.5m at a speed of 20.4m/s. The string is pulled in and the speed of the rock increases. When the string is 1m long and the speed of the rock is 51m/s, the string breaks. What is the breaking strength of the string?

17. 16. A penny of mass 3.1g rests on a small 20g block supported by a spinning disk. If the coefficients of friction between the block and the disk are 0.75(static) and 0.64(kinetic) while those for the penny and block are 0.45(kinetic) and 0.52(static), what is the maximum rate of rotation (in rpm) that the disk can have before either the block or the penny starts to slip?
12.0cm

18. 17. An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away. The coefficient of static friction between the person and the wall is μ, and the radius of the cylinder is R.
Show that the maximum period of revolution necessary to keep the person from falling is T=(4π2Rμ / g)2
Obtain a numerical value for T.

19. 18. Suppose air resistance is negligible for a golf ball
18. Suppose air resistance is negligible for a golf ball. A golfer tees off from a location precisely at Φ=35° north latitude. He hits the ball due south, with range 285m. The ball’s initial velocity is at 48° above the horizontal.
For what length of time is the ball in flight?

20. 18.(continued) The cup is due south of the golfer’s location, and he would have a hole in one if the Earth were not rotating. The Earth’s rotation makes the tee move in a circle of radius REcosΦ=(6.37x106m)cos35° completing one revolution each day.
Find the eastward speed of the tee, relative to the stars.

21. 18.(continued) The hole is also moving eastward, but is 285m farther south and thus a slightly lower latitude Φ. Because the hole moves eastward in a slightly larger circle, its speed must be greater than that of the tee.
By how much does the hole’s speed exceed that of the tee?

22. 18.(continued) During the time the ball is in flight, it moves both upward and downward, as well as southward with projectile motion, but it also moves eastward with the speed you found in part b. The hole moves to the east at a faster speed, however pulling ahead of the ball with the relative speed you found in part c.
How far to the west of the hole does the ball land?

23. REcosΦ
Golf ball trajectory RE

24. 19. A single bead can slide with negligible friction on a wire that is bent into a circle of radius 15cm. The circle is always in a vertical plane and rotates steadily about its vertical diameter with a period of 0.45s. The position of the bead is described by the angle θ that the radial line from the center of the loop to the bead makes with the vertical.
At what angle up from the lowest point can the bead stay motionless relative to the turning circle?
What if the period of rotation is 0.85s? θ

25. 20. A model airplane of mass 0
20. A model airplane of mass 0.75kg flies in a horizontal circle at the end of a 60m control wire, with a speed 35m/s. Compute the tension in the wire if it makes a constant angle of 20° with the horizontal.
20°
Lift
20° mg T