Tarzan, who weighs 669 N, swings from a cliff at the end of a convenient vine that is 21 m long. From the top of the cliff to the bottom of the swing, he descends by 3.2 m. The vine will break if the force on it exceeds 950 N. (a) Does the vine break? O Yes O No (b) What is the greatest force on the vine during the swing? N

1. The piston hydraulic system can lift very heavy objects with a force significantly lower than that of direct lifting. Imagine a system in which the cross-sectional area of the piston is rectangular rather than a typical circle. The cross-sectional area of the small piston is 20 cm × 40 cm, while the cross-sectional area of the large piston is 2.5 meters × 6 meters. (a) How much force would need to be applied to the smaller piston to lift a 1300-kg car? (Ignore any height differences in the fluid) (b) Use proportional reasoning, order of magnitude, and/or related quantities sense-making techniques to determine if your answer to (a) is reasonable?

Jumping up before the elevator hits. After the cable snaps and the safety system fails, an elevator cab free-falls from a height of 34 m. During the collision at the bottom of the elevator shaft, a 90 kg passenger is stopped in 6.0 ms. (Assume that neither the passenger nor the cab rebounds.) (a) What is the magnitude of the impulse on the passenger during the collision? N's (b) What is the magnitude of the average force on the passenger during the collision? N Suppose the passenger were to jump upward with a speed of 6.5 m/s relative to the cab floor just before the cab hits the bottom of the shaft. Assume the same stopping time as above. (c) What is the magnitude of the impulse on the passenger during the collision? N•s (d) What is the magnitude of the average force on the passenger during the collision? N

Consider a disc of mass M with a radius of 0.5 m that is lying on a slope at a 45-degree angle to the horizontal. It grips the hill well and does not slide. The disc is designed in such a way that its mass per unit area, (r), equals r1/2 kg m2, where r is the disc's radial distance in metres from its axis. Calculate the disk's mass.