Tension

A box weighing 100 N is pushed on a horizontal floor A box weighing 100 N is pushed on a horizontal floor. The coefficient of kinetic friction is 0.2. What acceleration will result if a person applies a horizontal force of 40 N? Don’t even begin to calculate anything until you have drawn a FBD!!!!!!! Warm-Up

Warm-Up Horizontally: Fnet = Fapplied - Ffriction Fnet = 40 - (0.2) (100) = 20 N Now, we want to find the acceleration using F = ma F = m a 20 = 10.2 a where m= W/g a = 1.96 m/s2 Warm-Up

Forces are often applied by means of cables or ropes that are used to pull an object. A force, T, is applied to the right end of a rope attached to a box. Each particle in the rope in turn applies a force to its neighbor. As a result the force is applied to the box. Tension

How does the tension in the left end of the rope compare with the tension in the right end? Who wins at tug of war?

Which rope sustains the greater tension Which rope sustains the greater tension? (three people pull just as hard in both cases) Who wins at tug of war?

When we look at problems with tension, we assume that we are using a “mass-less” rope. No net force is needed to accelerate a “mass-less” rope, so we can ignore it (otherwise you need to use calculus!) Assumptions

An elevator has a mass of 1000kg. It accelerates upward at 3m/s2 An elevator has a mass of 1000kg. It accelerates upward at 3m/s2. What is the force, FT, exerted by the cable on the elevator? FT (tension from the cable) ∑F = FT - FW = ma F T – 1000(9.8) = 1000(3) FT = 12,800 N FW (weight of elevator) Tension Example

An elevator has a mass of 1000kg. The elevator is at rest An elevator has a mass of 1000kg. The elevator is at rest. What is the force, FT, exerted by the cable on the elevator? FT (tension from the cable) ∑F = FT - FW = ma F T – 1000(9.8) = 0 FT = 9,800 N FW (weight of elevator) Tension Example

The ability of a mass-less rope to transmit tension undiminished from one end to the other is NOT affected when the rope passes around a pulley Pulleys

The ability of a mass-less rope to transmit tension undiminished from one end to the other is NOT affected when the rope passes around a simple pulley (one end is stationary) Pulleys

A window washer on a scaffold is hoisting the scaffold up the side of a building by pulling downward on a rope. The pulling force is 540N and the mass of the worker and scaffold is 155kg. What is the acceleration of the unit? Example

Equilibrium An object is in equilibrium when it has zero acceleration. Zero acceleration means constant velocity. (0 m/s is also constant velocity) Equilibrium means that the forces are balanced in each direction (x, and y) ΣFx = 0 ΣFy = 0 Equilibrium

Equilibrium Make sure to resolve all vectors into x- and y-components. ΣFx = 0 ΣFy = 0 Equilibrium

An object is NOT in equilibrium if it is accelerating, meaning there is an unbalanced force(s) Make sure to resolve all vectors into x- and y-components. ΣFx = max ΣFy = may Use a triangle to find the resultant acceleration Non-Equilibrium