18. Figure P10.18 shows the drive train of a bicvcle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter. Calculate (a) the speed of a link of the chain relative to the bicycle frame, (b) the angular speed of the bicycle wheels, and (c) the speed of the bicycle rela- tive to the road. (d) What pieces of data, if any, are not necessary for the calculations? Rear sprocket Pedal crank Front sprocket Chain Fiqure P10.18

The pulley in the figure has radius R = 1.0m and moment of inertia I = 10kg.m2. The block of mass m = 100 kg is displaced down a distance h from its equilibrium position, and is released from rest at t = 0. Determine the period of oscillation of the pulley. Consider that (k = 1000 N / m)

Engineers are designing a system by which a falling mass m imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum (the figure (Figure 1)). There is no appreciable friction in the axle of the drum, and everything starts from rest. This system is being tested on earth, but it is to be used on Mars, where the acceleration due to gravity is 3.71 m/s2. In the earth tests, when m is set to 13.0 kg and allowed to fall through 5.00 m, it gives 300.0 J of kinetic energy to the drum. If the system is operated on Mars, through what distance would the 13.0-kg mass have to fall to give the same amount of kinetic energy to the drum? How fast would the 13.0-kg mass be moving on Mars just as the drum gained 300.0 J of kinetic energy?

1. A 97 g ball bobbing up and down on the ocean as the waves roll by has a vertical position that can be described as a function of time by x(t) = cos(10t). What is the force on the ball at a time of 4.6 seconds? Note: The argument of the cosine function is in radians. Hint: Don't forget the sign of the force. F = 6.74 X√ N