Do Now Two people exert a 10 Newton force for 2 meters. Person 1 exerts the force at a 50 degree angle. Calculate the work done on the box by each person. Person 1  Person 2 W = Fdcosθ W = Fdcosθ = (10N)(2m)cos50˚ = (10N)(2m)cos0˚ = 12.9 J = 20 J

Net Work 12) An object is pulled by a 20N force due east for 5 meters and then due north by the same force for 3 meters. How much work was done? W1 = (20N)(5m) = 100 J W2 = (20N)(3m) = 60 J R WT= W2 + W3 = 160 J 3m 5m Note: The net work is related to the path traveled, It is NOT related to the resultant displacement.

Lifting 14) I decide to get my pet frog to do a little weight lifting (but I’m going to start him off slow!). He lifts 2 kg up from the floor, over his head 2 cm. How much work did he do? Flift = Weight W = F·d cosθ Flift = mg = 2kg(9.8m/s2) Flift = 19.6 N W = (19.6N)(0.02m) Weight W = 0.392 J

Why is it easier to lift the boulder with this simple machine than to pick it up directly? Does it take less Work to lift the boulder this way?

4 J 4 J Simple Machine “Lever” 1 m 4 m Input Work = Output Work Input Force = 1 N 4 m Output Force = 4 N Input Work = Output Work W= 1N x 4m W= 4N x 1m 4 J 4 J

Distance of Applied Force Distance of Output Other Types Of Levers Distance of Applied Force Distance of Output Output Force Input Force “Effort from Hands”

In sports: Baseball bats, golf clubs, hockey sticks, … Simple machines don’t change the amount of work we do, but it can make work “easier” to do. In sports: Baseball bats, golf clubs, hockey sticks, … http://science360.gov/obj/video/c5be5456-2e39-49a7-8118-218868df89eb/work-energy-power

Compound pulleys reduce the force needed to do work. What distance would the rope have to be pulled to make the weight rise 1 meter? W = Fd W = Fd 100 J = (25N)d W = (100N)(1m) d = (100J)/(25N) W = 100 J d = 4m

15) The box in the diagram below needs to be raised a distance of 50 meters. How much work is required to lift the box assuming the pulley is frictionless? Begin by calculating the force necessary to move the object. x F 20kg

Graphs 16) What does the slope of a Force versus Displacement graph represent? Write down a formula that uses the variables on the x and y axis Force (N) Displacement (m)

Graphs 17) What does the area under the curve represent? How do you find the area? Force (N) AREA Displacement (m)

Graphs 18) How much work was done on the 5 kg object represented by the graph below? Force (N) Displacement (m) 5 10 2 4 6 8 10 12 2.5 7.5

Graphs 19) A Changing force acts on an object represented by the graph below. How much work was done on the object? Force (N) Displacement (m) 5 10 2 4 6 8 10 12 2.5 7.5

What is Power? Power is defined as the rate at which work or energy is done or transformed.     = F · v

Units of Power 20) What are the units for Power? Work is measured in joules, time in seconds Power is measured in Watts. We will examine mechanical power rather than Electrical power.

Power Power is a Scalar quantity, no direction 21) What are some common devices that do work and produce/use mechanical power? Examples : Motors, heaters and other machines. 22) Question? Is Power a vector or scalar quantity? Work is scalar, time scalar. Power is a Scalar quantity, no direction

Power 23) How long would it take a machine to do 1,000J of work if the power rating on the machine is 75 watts?

Sample problem 25) A motor has an output of 20 watts. When the motor is working at full capacity, how long will it take to lift a 10 Newton box 50 meters?

Sample Problem 26) A student with a mass of 66.0 kg climbs up a ladder in 44.0 s. If the distance between the base and the top of the ladder is 14.0 m, how much power will the student deliver by climbing the stairs? The force necessary to climb the ladder is equal to the weight of the student.

Conceptual 27) Examine the Power formula below, How can we re-write it in relation to movement? As the velocity of an object increases, does the rate at which energy is used increase or decrease assuming a constant force? Answer: Power Increases

Power 28) A 45kg cyclist climbs a hill at a constant speed of 2.5m/s by applying an average force of 85 Newtons. How much power does the cyclist use?

Graphs 29) What does the slope of a Work vs. Time graph represent? Write down a formula that uses the variables on the x and y axis Work(J) Time s 5 10 2 4 6 8 10 12 2.5 7.5

Graph 30) How much power is developed by the system represented by the graph below? Work(J) Time s 5 10 2 4 6 8 10 12 2.5 7.5

31) What is the power of the Electric motor? Pulley motor d=10m t = 20seconds 1000kg