# Study of unbalanced forces

Kinetics, the study of unbalanced forces causing motion, can be analyzed by three methods: inertia force or torque (dynamic equilibrium), work and energy, and impulse and momentum.

Consider the following as you complete your assignment:

For linear motion the inertia force is

Equal to ma

Acting through the center of gravity

Opposite in direction to the acceleration

For rotational motion the inertia torque is

Equal to C

Opposite in direction to the angular acceleration

For a plane motion problem such as a rolling cylinder, try to

Equate or relate linear acceleration to angular acceleration.

Take moments at the rolling point of contact with the surface.

Questions

13–1.

Determine the acceleration of the 150-lb block in Figure P13–1 if the coefficient of kinetic friction is 0.4.

13–3.

A 130-kg cart is accelerated horizontally by a 250-N force pulling at an angle of 20° above horizontal. Neglecting rolling resistance, determine the acceleration of the cart.

13–7.

At what maximum acceleration rate can a 500-N test-strength cable lift a 40-kg mass?

13–8.

What force does a 180-lb man exert on the floor of an elevator that is moving downward and decelerating at 15 ft/s^2?

13–20.

The coefficient of kinetic friction for mass B in Figure P13–20 is 0.25. Determine the acceleration of mass A if it has a mass of (a) 30 kg and (b) 50 kg.

13–36.

A 1000-kW generator has a 3500-lb rotor that is accelerated from rest to 3600 rpm in 10 seconds. Determine the torque required. Assume the rotor to be a solid cylinder 40 in. in diameter.

13–41.

A 150-mm-diameter shaft with a mass of 20 kg is rotating at 900 rpm. A pulley mounted on the shaft has a mass moment of inertia of 0.15 kg m^2. If the shaft and the pulley coast to a stop due to a tangential frictional force of 8 lb at the outer radius of the shaft, determine the time required.