The crate has a mass of $80 \mathrm{~kg}$ and is being towed by a chain which is always directed at $20^{\circ}$ from the horizontal as shown. Determine the crate's acceleration in $t=2 \mathrm{~s}$ if the coefficient of static friction is $\mu_s=0.4$, the coefficient of kinetic friction is $\mu_k=0.3$, and the towing force is $P=\left(90 t^2\right) \mathrm{N}$, where $t$ is in seconds.

The force of the motor M on the cable is shown in the graph. Determine the velocity of the 400-kg crate A when t=2s.

The $400-\mathrm{kg}$ mine car is hoisted up the incline using the cable and motor $M$. For a short time, the force in the cable is $F=\left(3200 t^2\right) \mathrm{N}$, where $t$ is in seconds. If the car has an initial velocity $v_1=2 \mathrm{~m} / \mathrm{s}$ when $t=0$, determine the distance it moves up the plane when $t=2 \mathrm{~s}$.

Team $A$ and team $B$ consist of four members of total mass $320 \mathrm{~kg}$ and $330 \mathrm{~kg}$, respectively. If the average coefficients of static and kinetic friction for team $A$ are $\mu_n=0.52$ and $\mu_k=$ $0.5$, and for team $B, \mu_s=0.48$ and $\mu_k=0.46$, which team will win the tug of war? Also, what is the acceleration of the losing team if the winning team develops its maximum static friction force?

Block A starts from rest at $t=0$ and moves downward with a constant acceleration of $6 \mathrm{in} / \mathrm{s}^2$. Knowing that block $B$ moves up with a constant velocity of $3 \mathrm{in} . / \mathrm{s}$, determine (a) the time when the velocity of block $C$ is zero, (b) the corresponding position of block $C$.

A motorist is traveling at 54 km/h when she observes that a traffic light 240 m ahead of her turns red. The traffic light is timed to stay red for 24 s. If the motorist wishes to pass the light without stopping just as it turns green again, determine (a) the required uniform deceleration of the car, (b) the speed of the car as it passes the light.

A steam turbine operates adiabatically with a steam rate of $25 kg \cdot s^{−1}.$ The steam is supplied at 1300 kPa and $400^\circ C$ and discharges at 40 kPa and $100^\circ C.$ Determine the power output of the turbine and the efficiency of its operation in comparison with a turbine that operates reversibly and adiabatically from the same initial conditions to the same final pressure.

A steam turbine operates adiabatically at a power level of 3500 kW. Steam enters the turbine at 2400 kPa and $500^{\circ} \mathrm{C}$ and exhausts from the turbine as saturated vapor at 20 kPa. What is the steam rate through the turbine, and what is the turbine efficiency?

Steam enters a nozzle at 800 kPa and $280^\circ C$ at negligible velocity and discharges at a pressure of 525 kPa. Assuming isentropic expansion of the steam in the nozzle, what is the exit velocity and what is the cross-sectional area at the nozzle exit for a flow rate of $0.75 \mathrm{kg} \cdot \mathrm{s}^{-1} ?$

Steam enters a nozzle at 400 degree C and 800 kPa with a velocity of 10 m / s, and leaves at 375 degree C and 400 kPa while losing heat at a rate of 25 kW. For an inlet area of 800 cm $^2$, determine the velocity and the volume flow rate of the steam at the nozzle exit.

Steam enters a nozzle at 400$^\circ{}$C and 800 kPa with a velocity of 10 m/s, and leaves at 375$^\circ{}$C and 400 kPa while losing heat at a rate of 25 kW. For an inlet area of 800 cm^2, determine the velocity and the volume flow rate of the steam at the nozzle exit. Answers: 260 m/s, 1.55 m^3/s

Steam enters a nozzle at $400^\circ C$ and 800 kPa with a velocity of 10 m/s, and leaves at $300^\circ C$ and 200 kPa while losing heat at a rate of 25 kW. For an inlet area of $800 cm^2,$ determine the velocity and the volume flow rate of the steam at the nozzle exit.

Steam enters a converging nozzle at 800 kPa and $280^\circ C$ with negligible velocity. If expansion is isentropic, what is the minimum pressure that can be reached in such a nozzle, and what is the cross-sectional area at the nozzle throat at this pressure for a flow rate of $0.75 \mathrm{kg} \cdot \mathrm{s}^{-1} ?$

Block $A$ has a mass of $60 \mathrm{~kg}$ and rests on block $B$, which has a mass of $30 \mathrm{~kg}$. If the coefficients of static and kinetic friction are indicated in the figure. determine the largest horizontal force $\mathbf{P}$ which can be applied to block $B$ so that block $A$ does not slip on block $B$ while block $B$ slides.