Kinetic Energy, Potential Energy & Conservation of Energy

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1 Kinetic Energy, Potential Energy & Conservation of Energy Level : Conceptual Physics Teacher : Kim Kinetic Energy (K) If an object is in motion, it has the energy of motion, or kinetic energy. The kinetic energy of an object depends on the mass of the object as well as its speed. K = 1 2 mv2 [J] Q1) If a 5kg object is moving with a constant speed of 10m/s, what is the kinetic energy of the a) 200J b) 250J c) 300J d) 360J Q2) If a 5kg object is moving with a constant speed of 12m/s, what is the kinetic energy of the a) 200J b) 250J c) 300J d) 360J Q3) If an object of mass 5kg in motion has a kinetic energy of 200J, what is the speed of the a) 80.0m/s b) 43.5m/s c) 8.9m/s d) 4.5m/s Q4) If an object of mass 20kg in motion has a kinetic energy of 200J, what is the speed of the a) 80.0m/s b) 43.5m/s c) 8.9m/s d) 4.5m/s *~ Observe Video on Kinetic Energy & Potential Energy

2 Gravitational Potential Energy(U g) - When an object is lifted and placed on top of a wall, we are doing work on that object. (lifting force vertical distance = work) - By doing work against restoring force(gravity), then we are storing energy into the object - The energy we stored is called Gravitational Potential Energy. The symbol for gravitational potential energy is U g. F lift Lifting an object means doing work on the object - Exerting a force over a certain distance - More distance the block is lifted, the more work is being done - The more work is being done on the object means having more energy - The higher the object is being lifted, more energy is being stored => Gravitational potential energy is directly proportional to the vertical distance(=height) Gravitational Potential energy (U g ) = mgh where m is the mass, g=9.8m/s 2, h is height and the unit for energy is Joules[J] - Gravitational potential energy is often called energy of position while kinetic energy is the energy of motion Q5) A book is on the floor. You lift the book and place on your desk. How much gravitational potential energy(u g) did you store in the book? Mass of the book is 0.2kg, the height of the desk from the floor is 0.9m and g=9.8m/s 2. a) 1.76J b) 4.12J c) 7.89J d) 10.45J Q6) If you now place the same book (m=0.2kg) on the top of the book shelf, where the height of the book shelf is 2.1m from the floor, how much gravitational potential energy(u g) did you store in the book this time? a) 1.76J b) 4.12J c) 7.89J d) 10.45J Potential Energy in General - Whenever you do work against a restoring force, you are storing energy. - Lifting something means applying a force against the force of gravity that is trying to pull the object back down to its original position - This stored energy can be used for later use. Hence, called potential energy. - If an object has potential energy, once released, that stored energy will be converted into kinetic energy

3 **Conservation of Mechanical Energy Energy cannot be created or destroyed. It can be transformed from one form into another, but the total amount of energy never changes Q7) If you drop a ball from a certain height, does U g increases or decrease? Why? a) Increase b) decrease c) stays the same Explanation => Q8) When a ball is falling, does the kinetic energy increase or decrease? Why? a) Increase b) decrease c) stays the same Explanation => The sum of two energies, kinetic and gravitational potential energy is called total Mechanical Energy(E) When an object falls, the potential energy decreases while the kinetic energy increases, but the total mechanical energy remains constant throughout the motion E = K i + U gi = K f + U gf If you drop a ball from a certain height, the gravitational potential energy(u g) decreases and the kinetic energy(k) increases, but the total mechanical energy is conserved. *~ U g = mgh K = 1 2 mv2 ~* m=10kg, h=10.2m Ug =1000J K=0J Total Energy = Ug + K = 1000J h Ug =500J K=500J Total Energy = Ug + K = 1000J Ug =250J K=750J Total Energy = Ug + K = 1000J Ug =0J K=1000J Total Energy = Ug + K = 1000J

4 K = 1 mv² Ug = mgh Ki + Ugi = Kf + Ugf 2 Q9) An object of mass 10kg is lifted at a height of 10m. i) What is the gravitational potential energy of the object at that height? What is the kinetic energy at that height? ii) When the object falls 5m, what is the gravitational potential energy and kinetic energy at that height? What is the speed at that height? iii) When the object falls 8m, what is the gravitational potential energy and kinetic energy at that height? What is the speed at that height? Q10) An object of mass 5.3kg is lifted at a height of 4.6m. i) What is the gravitational potential energy of the object at that height? What is the kinetic energy at that height? ii) When the object falls 2.2m, what is the gravitational potential energy and kinetic energy at that height? What is the speed at that height? iii) When the object falls 3.5m, what is the gravitational potential energy and kinetic energy at that height? What is the speed at that height?

5 K = 1 mv² Ug = mgh Ki + Ugi = Kf + Ugf 2 Energy is path independent Q11) A child rides on a smooth slide of a height of 2m. The child starts from rest at the top. Determine the speed at the bottom a) 8.4m/s b) 6.3m/s c) 5.1m/s d) 4.6m/s Additional Practice Questions 1. An apple with a mass of 0.1kg falls off a tree branch with a height of 2.75m. Find the speed of the apple when it hits the ground? a) 7.3m/s b) 8.8m/s c) 9.4m/s d) 12.4m/s 2. A bowling ball with a mass of 5kg falls off a shelf with a height of 2m. How much kinetic energy would the bowling ball have when it has fallen halfway to the floor? a) 82J b) 69J c) 53J d) 49J

6 K = 1 mv² Ug = mgh Ki + Ugi = Kf + Ugf 2 3. A roller coaster of mass 10000kg starts from rest at the top of an 18m hill. The car travels to the bottom of the hill and continues up the next hill that is 10m high. h=18m A B h=10m How fast is the car moving at the bottom? That is, position A? a) 6.4m/s b) 8.1m/s c) 12.5m/s d) 18.8m/s How fast is the car moving at the top of the 2 nd hill? That is, position B? a) 6.4m/s b) 8.1m/s c) 12.5m/s d) 18.8m/s 4. A 0.8kg pendulum bob on a 2m cord is pulled sideways until pendulum bob is h=0.4m above position B. Find the speed of the bob as it passes through the position B after being released at rest. Position A is the maximum height and the position B will the lowest point of the bob. a) 2.2m/s b) 2.8m/s c) 3.5m/s d) 4.4m/s B A h=0.4m

Potential Energy & Conservation of Energy

Potential Energy & Conservation of Energy Level : Physics I Teacher : Kim Work and Change in Energy If we rearrange the Work-Kinetic Energy theorem as follows K i +Fcosφ d = K f => Fcosφ d = K f - K i