KOP: Force and Acceleration - General Questions

A particle having a mass of 1.5 kg, moves along a three-dimensional path defined by the equations r = 94 + 3t) m,  = (t² + 2) rad, and z = (6 - t³) m, where t is in seconds, and the z-axis is vertical. Determine the r, , and z components of force which the path exerts on the particle when t = 2 s.

Each of the three barges has a mass of 30 Mg, whereas the tugboat has a mass of 12 Mg. As the barges are being pulled forward with a constant velocity of 4 m/s, the tugboat must overcome the frictional resistance of the water, which is 2 kN for each barge and 1.5 kN for the tugboat. If the cable between A and B breaks, determine the acceleration of the tugboat.

The spool, which has a weight of 2lb, slides along the smooth horizontal spiral rod, r = (2) ft, where  is in radians. If its angular rate of rotation is constant and equals  = 4 rad/s, determine the tangential force P needed to cause the motion and the normal force that the spool exerts on the rod at the instant  = 90°.

A smooth can C, having a mass of 2 kg, is lifted from a feed at A to a ramp at B by a forked rotating rod. If the rod maintains a constant angular motion of  = 0.5 rad/s, determine the force which the rod exerts on the can at the instant  = 30°. Neglect the effects of friction in the calculation. The ramp from A to B is circular, having a radius of 700 min.

A truck T has a weight of 8,000 lb and is traveling along a portion of a road defined by the lemniscate r² = 0.2(106) cos 2 , where r is measured in feet and  is in radians. If the truck maintains a constant speed of vr = 4 ft/s, determine the magnitude of the resultant frictional force which must be exerted by all the wheels to maintain the motion when  = 0.

The pendulum bob B has a weight of 5 lb and is released from rest in the position shown,  =0°. Determine the tension in string BC just after the bob is released,  = 0°, and also at the instant the bob reaches point D,  = 45°.

A block having a mass of 2 kg is placed on a a spring scale located in an elevator that is moving downward. If the scale reading, which measures the force in the spring, is 20 N, determine the acceleration of the elevator. Neglect the mass of the scale.

A tobbogan and rider have a total mass of 100 kg and travel down along the (smooth) slope defined by the equation y = 0.2x². At the instant x = 8 m, the toboggan's speed is 4 m/s. At this point, determine the rate of increase in speed and the normal force which the toboggan exerts on the slope. Neglect the size of the toboggan and rider for the calculation.