Essential Question: How do you calculate potential and kinetic energy? Lesson 5.2 Energy Essential Question: How do you calculate potential and kinetic energy?

You go to an amusement park and wait in line to ride your favorite roller coaster. What happens when you go from the start of the ride to the bottom of the first hill?

What is energy? Energy is the ability to do work.

What is kinetic energy? The energy of an object that is due to the object’s motion

What determines kinetic energy? The speed and mass determine an object’s kinetic energy. It’s a scalar quantity and is measured in joules. When solving problems, the mass must be measured in kilograms and the speed measured in meters per second.

How do you calculate kinetic energy? 𝐾𝐸= 1 2 𝑚 𝑣 2 The kinetic energy of an object is equal to one-half the mass times the velocity squared.

A 6. 0 kg cat runs after a mouse at 10. 0 m/s A 6.0 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy?

What is the speed of an 8.0× 10 4 kg airliner with a kinetic energy of 1.1× 10 9 J?

What is the speed of a 0.145 kg baseball if its kinetic energy is 109 J?

A car has a kinetic energy of 4 A car has a kinetic energy of 4.32× 10 5 J when traveling at a speed of 23 m/s. What is its mass?

A 7. 00 kg bowling ball moves at 3. 00 m/s. How fast must a 2 A 7.00 kg bowling ball moves at 3.00 m/s. How fast must a 2.45 g table-tennis ball move in order to have the same kinetic energy as the bowling ball? Is this speed reasonable for a table-tennis ball in play?

What is the relationship between work and energy? 𝑊 𝑛𝑒𝑡 =𝐹∆𝑥=𝑚𝑎∆𝑥 Recall 𝑣 𝑓 2 = 𝑣 𝑖 2 +2𝑎∆𝑥 So 𝑎∆𝑥= 𝑣 𝑓 2 − 𝑣 𝑖 2 2 𝑊 𝑛𝑒𝑡 =𝑚 𝑣 𝑓 2 − 𝑣 𝑖 2 2 Therefore 𝑊 𝑛𝑒𝑡 = 1 2 𝑚 𝑣 𝑓 2 − 1 2 𝑚 𝑣 𝑖 2

Work-Kinetic Energy Theorem The net work done by all the forces acting on an object is equal to the change in the object’s kinetic energy.

When you use the work-kinetic energy theorem, you must include all the forces that do work on the object in calculating the net work done. It allows us to think of kinetic energy as the work that an object can do while the object changes speeds or as the amount of energy stored in the motion of the object.

On a frozen pond, a person kicks a 10 On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10?

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 352 J?

A 2.0× 10 3 kg car accelerates from rest under the actions of two forces. One is a forward force of 1140 N provided by the traction between the wheels and the road. The other is a 950 N resistive force due to various frictional forces. Use the work-kinetic energy theorem to determine how far the car must travel for its speed to reach 2.0 m/s.

A 75 kg bobsled is pushed along a horizontal surface by two athletes 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 potential energy? It is stored energy; an object that has the potential to move because of its position relative to some other location. It is the energy associated with an object because of the position, shape or condition of the object.

Potential energy depends not only on the properties of an object but also on the object’s interaction with its environment.

What is gravitational potential energy? The potential energy stored in the gravitational fields of interacting bodies. Gravitational potential energy depends on height from a zero level.

How do you find gravitational potential energy? 𝑃 𝐸 𝑔 =𝑚𝑔ℎ Gravitational potential energy is equal to the mass times free fall acceleration times the height.

Gravitational potential energy is measured in joules. It is a result of the object’s position, so it must be measured relative to some zero level. This zero level is arbitrary and is the vertical coordinate at which gravitational potential energy is defined to be zero.

What is elastic potential energy? The energy available for use when a deformed elastic object returns to its original configuration Elastic potential energy depends on distance compressed or stretched. It is stored in any compressed or stretched object, such as a spring or the stretched strings of a tennis racket or guitar.

The relaxed length is the length of a spring when no external forces are acting on it When an external force compresses or stretches the spring, elastic potential energy is stored in the spring. The amount of energy depends on the distance the spring is compressed or stretched from its relaxed length.

How do you find elastic potential energy? 𝑃 𝐸 𝑒𝑙𝑎𝑠𝑡𝑖𝑐 = 1 2 𝑘 𝑥 2 Elastic potential energy is equal to one half times the spring constant times the distance squared.

What is the spring constant (k)? A parameter that is a measure of a spring’s resistance to being compressed or stretched For a flexible spring, the spring constant is small. For a stiff spring, the spring constant is large. Spring constants have units of newtons divided by meters (N/m).

A 70.0 kg stuntman is attached to a bungee cord with an unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally stops, the cord has a stretched length of 44.0 m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of the bungee cord is 71.8 N/m, what is the total potential energy relative to the water when the man stops falling?

When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table. What is the gravitational potential energy associated with this mass relative to the table? What is the spring’s elastic potential energy if the spring constant is 400.0 N/m? What is the total potential energy of this system?

A spring with a force constant of 5. 2 N/m has a relaxed length of 2 A spring with a force constant of 5.2 N/m has a relaxed length of 2.45 m. When a mass is attached to the end of the spring and allowed to come to rest, the vertical length of the spring is 3.57 m. Calculate the elastic potential energy stored in the spring.

The staples inside a stapler are kept in place by a spring with a relaxed length of 0.115 m. If the spring constant is 51.0 N/m, how much elastic potential energy is stored in the spring when its length is 0.150 m?

A 40. 0 kg child is in a swing that is attached to ropes 2. 00 m long A 40.0 kg child is in a swing that is attached to ropes 2.00 m long. Find the gravitational potential energy associated with the child relative to the child’s lowest position under the following conditions: When the ropes are horizontal When the ropes make a 30.0° angle with the vertical At the bottom of the circular arc

How do you calculate kinetic and potential energy?