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Tension

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**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

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**Warm-Up Horizontally: Fnet = Fapplied - Ffriction**

Fnet = (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

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**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

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**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?

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**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?

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**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

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**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

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**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

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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

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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

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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

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**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

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**Equilibrium Make sure to resolve all vectors into x- and y-components.**

ΣFx = 0 ΣFy = 0 Equilibrium

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**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

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