1.
From t = 0 to t = 4.81 min, a man stands still, and from t = 4.81 min to t = 9.62 min, he walks briskly in a straight line at a constant speed of 1.71 m/s. What are (a) his average velocity vavg and (b) his average acceleration aavg in the time interval 1.00 min to 5.81 min? What are (c) vavg and (d) aavg in the time interval 2.00 min to 6.81 min?
(a) / Number / / Units /(b) / Number / / Units /
(c) / Number / / Units /
(d) / Number / / Units /
2.
The Zero Gravity Research Facility at the NASAGlennReseachCenter includes a 133 m drop tower. This is an evacuated vertical tower through which, among other possibilities, a 1 m diameter sphere containing an experimental package can be dropped. (a) How long is the sphere in free fall? (b) What is its speed just as it reaches a catching device at the bottom of the tower? (c) When caught, the sphere experiences an average deceleration of 35.0g as its speed is reduced to zero. Through what distance does it travel during the deceleration?
(a) / Number / / Units /(b) / Number / / Units /
(c) / Number / / Units /
3.
A 310-m-wide river has a uniform flow speed of 0.97 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 9.4 m/s with respect to the water. There is a clearing on the north bank 95 m upstream from a point directly opposite the clearing on the south bank. (a) At what angle, measured relative to the direction of flow of the river, must the boat be pointed in order to travel in a straight line and land in the clearing on the north bank? (b) How long will the boat take to cross the river and land in the clearing?
(a) / Number / / Units /(b) / Number / / Units /
4.
Figure 5-56 shows a man sitting in a bosun's chair that dangles from a massless rope, which runs over a massless, frictionless pulley and back down to the man's hand. The combined mass of man and chair is 96.7 kg. With what force magnitude must the man pull on the rope if he is to rise (a) with a constant velocity and (b) with an upward acceleration of 1.10 m/s2? (Hint: A free-body diagram can really help.) Problem continues below.
Fig. 5-56
Problem 60.
If the rope on the right extends to the ground and is pulled by a co-worker, with what force magnitude must the co-worker pull for the man to rise (c) with a constant velocity and (d) with an upward acceleration of 1.10 m/s2? What is the magnitude of the force on the ceiling from the pulley system in (e) part a (f) part b, (g) part c, and (h) part d?
(a) / Number / / Units /(b) / Number / / Units /
(c) / Number / / Units /
(d) / Number / / Units /
(e) / Number / / Units /
(f) / Number / / Units /
(g) / Number / / Units /
(h) / Number / / Units /
5.
In Fig. 6-52, a box of ant aunts (total mass m1 = 2.06 kg) and a box of ant uncles (total mass m2 = 4.46 kg) slide down an inclined plane while attached by a massless rod parallel to the plane. The angle of incline is θ = 28°. The coefficient of kinetic friction between the aunt box and the incline is μ1 = 0.206; that between the uncle box and the incline is μ2 = 0.120. Compute (a) the tension in the rod and (b) the common acceleration of the two boxes.
Fig. 6-52
Problem 68.
(b) / Number / / Units /
6.
A skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 19° with the horizontal. The rope moves parallel to the slope with a constant speed of 1.3 m/s. The force of the rope does 520 J of work on the skier as the skier moves a distance of 4.5 m up the incline. (a) If the rope moved with a constant speed of 1.6 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 4.5 m up the incline? At what rate is the force of the rope doing work on the skier when the rope moves with a speed of (b) 1.3 m/s and (c) 1.6 m/s?
(a) / Number / / Units /(b) / Number / / Units /
(c) / Number / / Units /
7.
In Fig. 7-48, a cord runs around two massless, frictionless pulleys. A canister with mass m = 44 kg hangs from one pulley, and you exert a force on the free end of the cord. (a) What must be the magnitude of if you are to lift the canister at a constant speed? (b) To lift the canister by 3.5 cm, how far must you pull the free end of the cord? During that lift, what is the work done on the canister by (c) your force (via the cord) and (d) the gravitational force? (Hint: When a cord loops around a pulley as shown, it pulls on the pulley with a net force that is twice the tension in the cord.)
Fig. 7-48
Problem 57.
(b) / Number / / Units /
(c) / Number / / Units /
(d) / Number / / Units /
8.
The cable of the 1900 kg elevator cab in Fig. 8-56 snaps when the cab is at rest at the first floor, where the cab bottom is a distance d = 4.4 m above a spring of spring constant k = 0.20 MN/m. A safety device clamps the cab against guide rails so that a constant frictional force of 6.9 kN opposes the cab's motion. (a) Find the speed of the cab just before it hits the spring. (b) Find the maximum distance x that the spring is compressed (the frictional force still acts during this compression). (c) Find the distance (above the point of maximum compression) that the cab will bounce back up the shaft. (d) Using conservation of energy, find the approximate total distance that the cab will move before coming to rest. (Assume that the frictional force on the cab is negligible when the cab is stationary.)
Fig. 8-59
Problem 65.
(b) / Number / / Units /
(c) / Number / / Units /
(d) / Number / / Units /
9.
A conservative force F(x) acts on a 1.9 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is graphed in Figure 8-70. When the particle is at x = 2.0 m, its velocity is –1.0 m/s. (a) What is F(x) at this position, including sign? Between what positions on the (b) left and (c) right does the particle move? (d) What is its particle's speed at x = 7.0 m?
Fig. 8-70
Problem 121.
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(c) / Number / / Units /
(d) / Number / / Units /