Physics chapter 7_2

Notice that kinetic energy is proportional to its

mass of an object.

gravatational potential energy

potential energy due to elevated position. Examples: Wreaking ball, water in an elevated reservoir, and raised ram of a pile driver.

Equal to work done

(Force required to move it upward x the vertical distance moved against gravity) in lifting it. We found previously that the work to lift something against gravity is (mgd) In equation form: Potential energy = mass x acceleration due to gravity x height = mgh

Conservation of energy examples

-Electrical energy is converted into mechanical energy in an electric motor -Mechanical energy is converted into electrical energy in a generator -Electrical energy is converted to thermal energy when we heat our house

Word problem for that equation is on

29:42

Another problem for that equation is on

30:40 and explained on 31:00

Homework q and a

https://www.chegg.com/homework-help/questions-and-answers/question-1-225-points-ball-rolling-incline-maximum-kinetic-energy-top-5-b-halfway-9-c-thre-q57808160?trackid=4e8e1660913e&strackid=003e5c7ee47d

Suppose the potential energy of a drawn bow is 50 joules and the kinetic energy of the shot arrow is 40 joules. Then A. energy is not conserved B. 10 joules go to warming the box C. 10 joules go to warming the target D. 10 joules are mysteriously missing.

B. 10 joules go to warming the bow Explanation: The total energy of the drawn bow, which includes the poised arrow, is 50 joules. The arrow gets 40 joules and the remaining 10 joules warms the box - still in the initial system. If no energy were lost to heat the kinetic energy of the shot arrow would also be 50 joules because of energy conservation.

The work done in bringing a moving car to a stop is the force of the tire friction x stopping distance. If the initial speed of the car is tripled, the stopping distance is? A. Also tripled B. Multiplied by a factor of six C. Multiplied by a factor of nine D. None of the above

C. Multiplied by a factor of nine Explanation: Three times the speed means nine times the kinetic energy and nine times the stopping distance.

Conservation of energy with a box and arrow

Consider the system of a bow and arrow. In drawing the box, we do work on the system and give it potential energy. When the bowstring is released, most of the potential energy is transferred to the arrow as kinetic energy and some as heat to the box.

The work done in bringing a moving car to a stop is the force of the tire friction x stopping distance. If the initial speed of the car is doubled, the stopping distance is? A. Actually less B. About the same C. Twice D. None of the above.

D. None of the above. Explanation: Twice the speed means four times the kinetic energy and four times the stopping distance.

Conservation of energy or Law of conservation of energy is

Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes.

A car moving at 50 km/hr skids 20 m with locked brakes. How far will the car skid with locked brakes if it were traveling at 150 km/hr? A) 20 m B) 60 m C) 90 m D) 120 m E) 180 m

Formula we will apply here v2 = u2 + 2aS v = 0 for both the cases, as the car is stopping by hence, u2 = - 2aS [ a is the acceleration] For the two cases, the equation becomes, u12 = -2aS1 & u22 = = 2aS2 hence, Dividing the above two equations we get, S2/S1 = u22/u12 or, S2/S1 = 1502/502 or, S2/S1 = (150/50)2 or S2/S1 = 32 =9 or S2 = 9 S1 = 9 x 20 m = 180 m option E is correct

work-energy theorem

Gain or reduction of energy is the result of work. For example: Work required to get up to a certain speed from rest. -The work done on the car is equal to the change in kinetic energy. Similarly, it takes work to slow or stop a car. The work done on the car is equal to the change in kinetic energy. In equation form: W = ΔKE

kinetic energy example to mass

If speed is kept constant, but the mass is doubled, then the kinetic energy will double. For example, 2 cars going 10 m/s but one car twice as massive. https://gyazo.com/184a6095204f5bcc3f75673392e6ed87

kinetic energy calculator

https://www.omnicalculator.com/physics/kinetic-energy

What are units of energy measured in?

Just like work energy is measured in Joules.

For any object or system the total mechanical energy is the sum of potential and kinetic energy

ME = PE + KE

A pile-driver ram with a mass of 255 kg falls 10 m and drives a post 0.1 m into the ground. The average impact force on the ram is (hint: first find the potential energy of the ram when it is raised. Then use energy conservation and the work-energy theorem). A) 2,499 N. B) 24,990 N. C) 249,900 N. D) 2,499,000 N.

Potential energy of the ram at 10 m above the ground = mgh = 255 x 9.8 x 10 = 24990 Joule Now when it falls over to the ground all the potential energy converts to kinetic energy. Now, with the help of this energy, it drives a post 0.1 m into the ground. Say the impact force by the ram on the post = F. So, the work done = F x 0.1 = 0.1 F According to work energy theorem, work done = change in kinetic energy hence, 0.1 F = 24,990 or, F = 249,900 N option c) is correct.

Which has greater kinetic energy, a 2000 kg car traveling at 30 km/hr or a 1000 kg car traveling at 60 km/hr? A) the 30 km/hr car B) the 60 km/hr car C) Both have the same kinetic energy. D) More information is needed about the distance traveled.

The Kinetic energy (K) of an object of mass 'm', moving with speed 'v' is given by K = ½ mv2 In the above equation first case m1 = 2000 kg, v1 =30 km/hr K1 = ½ m1 x v12 In the second case m2 = 1000 kg, v2 =60 km/hr K2 = ½ m2 x v22 Now, K2/K1 = (m2 x v22) / (m1 x v12) = (1000 x 602)/ (2000 x 302) or, K2/K1 = 3600/(2x900) or K2/K1 = 2 or, K2 = 2K1 B) is correct.

A car moves 4 times as fast as another identical car. Compared to the slower car, the faster car has a) 2 times the kinetic energy b) 4 times the kinetic energy c) 8 times the kinetic energy d) 16 times the kinetic energy

The Kinetic energy (K) of an object of mass 'm', moving with speed 'v' is given by K = ½ mv2 The kinetic energy is proportional to the square of the velocity. As the car is moving 4 times faster than an identical car, it (faster car) will have 42 or 16 times more kinetic energy.

Energy is

The property of a system that enables it to do work. -Anything that can turn into heat. Example: Electromagnetic waves from the sun

What is Mechanical energy?

is due to the position and motion or both.

potential energy

is held in energy in readiness with a potential for doing work

A skier starts from rest at the top of the slope. Assuming negligible friction how fast will the skier be going when she gets to the point marked X? https://gyazo.com/df2fea798852702b33395a9cfa746251 a) 21.7 m/s b) 24.0 m/s c) 48 m/s d) 25.0 m/s

We will use the conservation of mechanical energy principle here, which is as follows Potential Energy + Kinetic energy = Const. Let the speed of the skier at 'X' mark = v m/s Hence, (Potential Energy + Kinetic energy) top = (Potential Energy + Kinetic energy) 'X' mark m x g x 28 + 0 = m x g x 4 + ½ m x v2 [ Kinetic energy at top is zero, as it was at rest there] g x 28 = g x 4 + ½ v2 ½ v2 = 24 x g v2 = 48 x g v2 = 48 x 9.8 [ g= acceleration due to gravity = 9.8 m/s2 ] v2 = 470.4 v = 21.7 m/s (Ans)

Work-energy theorem being applied to decreasing speed

When a person applies brakes to a slow-moving car, work is being done on the car. The force applied to the car is the friction between the tires and the road, and we say that the road does work on the car. -The distance involved is called stopping distance. The equation on the video is 16:20

What are the two forms of energy?

kinetic and potential

What is kinetic energy?

energy of motion Depends on the mass of the object and the square of its velocity and is given by: Kinetic energy = 1/2 x mass x velocity x velocity https://gyazo.com/52dbc3e4928708e3364d9590942999fe

Energy transforms without net loss or net gain in operation of the pile driver - example

https://gyazo.com/111638b2e9350974b3981a5114a45324

A good example of potential energy in the video is at

https://gyazo.com/340cb254c2680c5bb71d79a3d9f3b939

Work energy theorem equations

https://gyazo.com/64cd4a2b9a17007efbb18fe877dd7a63

A pendulum swing (we ignore friction)

https://gyazo.com/dc7f48c9b5ffa7182c82d67ae40a2bbe

Example of using conversion of mechanical energy for two points

https://gyazo.com/e196ca630b7bfffc0d7992253e71e7ac

Kinetic energy is proportional to the square of the speed this means

that doubling the speed of an object requires 4 times the work.

kinetic energy example with velocity

the kinetic energy of an object is proportional to the square of its velocity. That means if the mass is kept constant but the speed is doubled, then the kinetic energy will be quadrupled! For example, consider 2 cars of the same mass, but one car is going twice as fast https://gyazo.com/64a4d89e7a7dc77ad8435be4353fd583

If we know the initial height of the pendulum we can calculate the velocity at any point in its swing. It is simplified even further if we want to find the velocity at the lowest point.

time stamp 26:49

Equations for velocity at point 1 is 0 and point 2 is 0

time stamp 27:14

A ball rolling down an incline has its maximum potential energy at a) The top b) A quarter of the way down c) Halfway down d) The bottom

when a ball rolls down an incline potential energy converts to kinetic energy. When it is at the top position the total energy is the potential energy. At the top position it is maximum Option a) is correct.

Examples of potential energy

•A stretched bow has stored energy that can do work on an arrow •A stretched rubber band of a slingshot has stored energy and is capable of doing work A wreaking ball does work when it demolishes a building.