Example 2. Example 1. Example 4. Example 3. Kinetic Energy. Kinetic Energy 11/19/15

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1 A tugboat pulls a ship with a constant net horizontal force of 5.00 x 10 3 N and causes the ship to move through a harbor. How much work is done on the ship if it moves a distance of 3.00 km? Example A weight lifter lifts a set of weights a vertical distance of.00 m. If a constant net force of 350 N is exerted on the weights, what is the net work done on the weights? A shopper in a supermarket pushes a cart with a force of 35 N directed at an angle of 5 downward from the horizontal. Find the work done by the shopper on the cart as the shopper moves along a 50.0 m length of aisle. If.0 J of work is done in raising a 180 g apple, how far is it lifted? Kinetic Energy Kinetic Energy (KE) is energy associated with an object that is in motion Kinetic energy depends on mass and the speed of that mass KE = 1/mv Kinetic Energy Kinetic Energy is known as the energy of motion. n KE = ½ mv If you double the mass, what happens to the kinetic energy? It doubles. If you double the velocity, what happens to the kinetic energy? It quadruples. Show units comparison 1

2 Calculate the speed of an 8.0 x 10 4 kg airliner with a kinetic energy of 1.1x10 9 J. Example What is the mass of a baseball if its kinetic energy is 109 J and it is traveling at 40 m/s? Kinetic Energy & Work Newton s nd Law of Motion (F net = ma) n v f v i = ad F net n Substituting for a: m F d n v f v i = net m n Multiplying both sides of the equation by ½ m n ½ mv f ½ mv i = F net d Kinetic Energy & Work The left side of the mathematical relationship is equal to the change in Kinetic Energy of the system. KE = ½ mv f ½ mv i The right side of the mathematical relationship is equal to the amount of Work done by the environment on the system. W = F net d Work Energy Theorem The Work-Energy Theorem states that the work done on an object is equal to its change in kinetic energy. ΔKE = W Note: this condition is true only when there is no friction. Work-Kinetic Energy Theorem Work-Kinetic Energy Theorem: the net work done on an object is equal to the change in the kinetic energy of the object Units: Joule (J) 1 Joule is equal to the amount of work done by a 1 Newton force over a displacement of 1 meter. 1 Nm 1 kg m /s

3 A student wearing frictionless in-line skates on a horizontal surface is pushed by a friend with a constant force of 45 N. How far must the student be pushed, starting from rest, so that her final kinetic energy is 35 J? Example A.0x10 3 kg car accelerates from rest under the actions of two forces. One is a forward force of 1140 N provided by traction between the wheels and the road. The other is a 950 N resistive force due to various frictional forces. Use the work-energy theorem to determine how far the car must travel for it s speed to reach.0 m/s. A.1x10 3 kg car starts from rest at the top of a driveway that is sloped at an angle of 0.0 with the horizontal. An average friction force of 4.0x10 3 N impedes the car s motion so that the car s speed at the bottom of the driveway is 3.8 m/s. What is the length of the driveway? A 75 kg bobsled is pushed along a horizontal surface by two athletes. After the bobsled is pushed a distance of 4.5 m starting from rest, its speed is 6.0 m/s. Find the magnitude of the net force on the bobsled. What is it? is measure of the amount of work done per unit of time. What are the units? Joule/second Watts P = W/t P = W / t OR since W = Fd we can say P = (Fd)/t since v = (d/t) we can say P= Fv is an alternative form of the power equation, and can be used to express instantaneous power when velocity is constant 3

4 11/19/15 Thought Question can also be converted to units of horsepower (hp) How many horses are in one horsepower? Note: 1 hp = 746 W coffee maker blender lawn mower Corvette Notes Example If Superman, at 90kg, jumps a 40m building in a single bound, how much work does Superman perform? If this occurs in 3s, what is his power output? Example A car with a mass of 1.50x103 kg starts from rest and accelerates to a speed of 18.0 m/s in 1.0 s. Assume that the force of resistance remains constant at N during this time. What is the average power developed by the car s engine? 0.75 hp 1.5 hp 5-6 hp 400 hp A 1.0x103 kg elevator carries a maximum load of kg. A constant frictional force of 4.0x103 N retards the elevator s motion upward. What minimum power, in kilowatts, must the motor deliver to lift the fully-loaded elevator at a constant speed of 3.00 m/s. A rain cloud contains.66x107 kg if water vapor. How long would it take for a.00 kw pump to raise the same amount of water to the cloud s altitude,.00 km? 4

5 How long does it take a 19 kw steam engine to do 6.8x10 7 J of work? 5

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