The physics associated with statics has considerable applications in engineering. As a mechanical engineer working for a tow-truck manufacturer, you have been asked to evaluate the purchase of a new line of towing cable. The supplier claims that, although its cables are not as strong as its competitors (maximum tension capability of 9110 lb), the cost savings make it a good investment. A schematic of the towing configuration is shown. The car weighs 6479 lb, which is as large as the company expects their tow trucks to service. The overall length L of the car is 10.1 ft, and the distance d between the midpoints of the front and back tires is 9.09 ft. The bottom of the car's frame is a height hf = 0.370 above the ground, and the car's center of mass is a height hCM = 1.50 above the bottom of the car's frame. The angle ϕ between the midpoint of the tires and the tow cable is 50.0∘. Assume the CM of the car is positioned exactly halfway across its length, the geometry of the wheels and front/rear of the car is symmetrical, and that the coefficient of friction between the road and tires is sufficient to maintain no acceleration in the system. Calculate the tension T in the cable just as the front of the car begins to lift off the ground. Assume that the front end rises at a constant velocity. T = lb Based on your results, what would you advise your company? The cable they are offering is more than adequate. The cost savings make this a worthwhile investment. The cable they are offering is too weak to use. I would decline the purchase.
A 82 kg man is riding on a 44 kg cart traveling at a speed of 1.9 m/s. He jumps off with zero horizontal speed relative to the ground. What is the resulting change in the cart's speed, including sign? Number Units
The crane shown in the figure is lifting a 309-kg crate upward with an acceleration of 3.49 m/s2. The cable from the crate passes over a solid cylindrical pulley at the top of the boom. The pulley has a mass of 247 kg. The cable ts then wound onto a hollow cylindrical drum that is mounted on the deck of the crane. The mass of the drum is 182 kg. and its radius (the same as that of the pulley) is 0.569 m. The engine applies a counterclockwise torque to the drum in order to wind up the cable. What is the magnitude of this torque? Ignore the mass of the cable. Number Units
In the figure, a block weighing 13.2 N, which can slide without friction on an incline at angle θ = 35.0∘, is connected to the top of the incline by a massless spring of unstretched length 0.330 m and spring constant 120 N/m. The block is initially at its equilibrium position. (a) How far from the top of the incline is the block's equilibrium point? (b) If the block is pulled slightly down the incline and released, what is the period of the resulting oscillations? (a) Number Units (b) Number Units
A ball of mass 0.198 kg with a velocity of 1.56 i^ m/s meets a ball of mass 0.294 kg with a velocity of −0.399 i^ m/s in a head-on, elastic collision. (a) Find their velocities after the collision. v→1f = m/s v→2f = m/s (b) Find the velocity of their center of mass before and after the collision. v→cm, before = m/s v→cm, after = m/s
A circuit contains an emf produced by a moving metal rod of charge 15.5 μC across a magnetic field of 0.28 T, shown in the diagram. This allows a 367 Ω light bulb to turn on. If the force on the metal rod is 4 N, what would be the current running across the circuit? The length of the rod L = 2.9 mm. The rails and rod have a negligible electrical resistance. (Hint: This is a 3 to 4 step problem. Start by working backwards. Try using the equation for what you're solving for, and then use equations to sub in missing info)
A thin rod of length 0.913 m and mass 249 g is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular speed 1.65 rad/s. Neglecting friction and air resistance, find (a) the rod's kinetic energy at its lowest position and (b) how far above that position the center of mass rises. (a) Number Units (b) Number Units
A young work crew is trying to quickly finish some touch-up painting to complete a job. Rather than setting up a secure work area, they decide to try a shortcut. Worker A will hold the far end of a 8.00 m work plank that weighs 114 N and is secured with a hinge on the opposite end. Worker B will stand on the plank 4.22 m from worker A. Worker B also brings up his paint can of mass mc = 3.58 kg, which he places 0.430 m from where he is standing on the plank (between the two workers). Worker A needs to supply 483 N of force to keep the end of the plank stable. The acceleration due to gravity is g = 9.81 m/s2. How much WB does worker B weigh? WB = N