Work, Power & Mechanical Advantage

What is Work?? Work is only done when a force causes a change in the position or the motion of an object The motion must be in the direction of the applied force. Work is a force applied over a distance

Work Equation W = F*d W = work F = force d = distance UNITS!! Force must be in Newtons, N Distance must be in meters, m Work is a Newton * meter = Joule (J)

Example Problem #1 Imagine a father playing with his daughter by lifting her repeatedly in the air. How much work does he do with each lift, assuming he lifts her 2.0 m and exerts an average force of 190 N? W = ? F = 190 N d = 2.0 m W = (190N)(2.0 m) W = 380 N*m = 380 J

Example Problem #2 A weightlifter exerts a force of 600 N to hold a barbell over his head. How much work does he do? W = ? F = 600N d = 0 m W = (600 N)(0 m) W = 0 J

And now time for a mini-Lab Who does the most work walking up stairs?

Power Which requires more work? Running up a flight of stairs or walking up a flight of stairs? Running and walking require the SAME amount of work even though running is more exhausting. Power measures work in relation to time.

Power Equation P = W/t P = Power W = Work t = time UNITS!!! Work is measured in Joules Time is measured in seconds Power = Joule/second = Watt (W)

Example Problem #1 It takes 100 kJ of work to lift an elevator 18 m. If this is done in 20 seconds, what is the average power of the elevator during this process? P = ? W = 100 kJ = 100,000 J t = 20 seconds P = 100,000J / 20 seconds = 5,000 J/s or 5,000 W

Time for mini-Lab, Part B Who has the most power??

Mechanical Advantage Is it easier to lift a car yourself or use a jack? Which requires more work? Answer: They require the SAME amount of work The jack makes the work easier by allowing you to apply less force at any given moment. Mechanical Advantage measures how much a machine multiplies force or distance.

Multiplying the Force Machines can change the direction of an input force. Machines can increase or decrease force by changing the distance over which force is applied (known as multiplying the force) A machine may allow you to apply a smaller force BUT you must move a greater distance.

Notice that the Work done is the same but the force is greater on the steeper slope.

Mechanical Advantage Equations MA = output Force/input Force MA = input Distance/output Distance UNITS!! Force must be in Newtons Distance must be in meters MA = N/N or m/m = NO UNIT!! A machine with an MA of greater than 1 multiplies the input force.

Example Problem #1 Calculate the mechanical advantage of a ramp that is 5.0 m long and 1.5 m high. Dealing with distances: MA = input d/output d MA = ? Input d = 5.0 m Output d = 1.5 m MA = 5.0 m/1.5 m MA = 3.3

Time for one more mini-Lab