The crate is at rest at point $A$ when it is nudged down the incline. If the coefficient of kinetic friction between the crate and the incline is $0.30$ from $A$ to $B$ and $0.22$ from $B$ to $C$, determine its speeds at points $B$ and $C$.

The radar tracking antenna oscillates about its vertical axis according to where is the constant circular frequency and is the double amplitude of oscillation. Simultaneously, the angle of elevation is increasing at the constant rate Determine the expression for the magnitude a of the acceleration of the signal horn (a) as it passes position A and (b) as it passes the top position B, assuming that θ = 0 at this instant.

The small slider A moves with negligible friction down the tapered block, which moves to the right with constant speed v = $v_0$. Use the principle of work-energy to determine the magnitude $v_A$ of the absolute velocity of the slider as it passes point C if it is released at point B with no velocity relative to the block. Apply the equation, both as an observer fixed to the block and as an observer fixed to the ground, and reconcile the two relations.

Collar A is free to slide with negligible friction on the circular guide mounted in the vertical frame. Determine the angle $\theta$ assumed by the collar if the frame is given a constant horizontal acceleration a to the right.

At a steady speed of 200 mi/hr along a level track, the racecar is subjected to an aerodynamic force of 900 lb and an overall rolling resistance of 200 lb. If the drivetrain efficiency is e = 0.90, what power P must the motor produce?

The 180-lb exerciser is beginning to execute some slow, steady bicep curls. As the tension T = 15 lb is developed against an exercise machine (not shown), determine the normal reaction forces at the feet A and B. Friction is sufficient to prevent slipping, and the exerciser maintains the position shown with center of gravity at G.

It is experimentally determined that the drive wheels of a car must exert a tractive force of 560 N on the road surface in order to maintain a steady vehicle speed of 90 km/h on a horizontal road. If it is known that the overall drivetrain efficiency is $e_{m}=0.70,$ determine the required motor power output P.

A train consists of a 400,000-lb locomotive and one hundred 200,000-lb hopper cars. If the locomotive exerts a friction force of 40,000 lb on the rails in starting the train from rest, compute the forces in couplers 1 and 100. Assume no slack in the couplers and neglect friction associated with the hopper cars.

Hot oil $(c_p = 2200 J/kg \cdot K)$ is to be cooled by water $(c_p = 4180 J/kg \cdot K)$ in a 2-shell-passes and 12-tube-passes heat exchanger. The tubes are thin-walled and are made of copper with a diameter of 1.8 cm. The length of each tube pass in the heat exchanger is 3 m, and the overall heat transfer coefficient is $340 W/m^2 \cdot K.$ Water flows through the tubes at a total rate of 0.1 kg/s, and the oil through the shell at a rate of 0.2 kg/s. The water and the oil enter at temperatures $18^\circ C$ and $160^\circ C,$ respectively. Determine the rate of heat transfer in the heat exchanger and the outlet temperatures of the water and the oil.

During a brake test, the rear-engine car is stopped from an initial speed of 100 km/h in a distance of 50 m. If it is known that all four wheels contribute equally to the braking force, determine the braking force F at each wheel. Assume a constant deceleration for the 1500-kg car.

The rod of the fixed hydraulic cylinder is moving to the left with a constant speed $v_A$ = 25 mm/s. Determine the corresponding velocity of slider B when $s_A$ = 425 mm. The length of the cord is 1050 mm, and the effects of the radius of the small pulley A may be neglected.

Refrigerant-134a enters an adiabatic compressor as saturated vapor at 160 kPa at a rate of 2 m^3/min and is compressed to a pressure of 900 kPa. Determine the minimum power that must be supplied to the compressor.

The 4-kg slider is released from rest in position A and slides down the vertical-plane guide. If the maximum compression of the spring is $k=20 \mathrm{kN} / \mathrm{m}$ observed to be 40 mm, determine the work Uƒ done by friction.

Instruments located at O are part of the groundtraffic control system for a major airport. At a certain instant during the takeoff roll of the aircraft P, the sensors indicate the angle $\theta = 50^{\circ}$ and the range rate $\dot{r}=140 \mathrm{ft} / \mathrm{sec}$. Determine the corresponding speed v of the aircraft and the value of $\dot{\theta}$.