### SAT Physics Energy, Work, and Power - Power

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**SAT Physics Energy, Work, and Power - Pow**er

**POWER**

Power, P,is the amount of work done over a period of time. It is the rate at which work is done. It is also the rate of energy use or energy generation. It can be calculated using the following equation.

P = Fv

Power has the units of watts (W). When you look at the top of a lightbulb, it is labeled in watts. A watt is the rate at which the lightbulb uses energy. Another way to express a watt is a joule per second. A 100-watt lightbulb uses 100 joules of energy every second. Power is a scalar quantity. It has magnitude but no direction.**Determining the Power Required to Lift an Object**

**WHAT'S THE TRICK?**

Power is the rate that work is done. Solve for work using the methods described in the previous section, and then divide by time. In this case, force and displacement are given. However, displacement is in units of centimeters. You must first convert centimeters into meters.

**Find the Power at a Constant Velocity**

**WHAT'S THE TRICK?**

This problem is similar to Example 7.8. However, this time the speed is given instead of the distance and time.

P= Fv

P = (10 N)(2.0 m/s) = 20 W

P = (10 N)(2.0 m/s) = 20 W

**CONSERVATION OF ENERGY**

Energy is always conserved in an isolated system. The amount of energy present at the start of a problem must remain constant throughout the entire problem. You must consider some important properties of energy to understand conservation of energy fully.

- Energy can transform from one type to another.
- Energy can transfer from one object to another.
- Energy can leave and enter a closed system as work.

**Conservative Forces**

The force of gravity, F , and the force of springs, F

_{s}, are examples of conservative forces. When conservative forces act, the total mechanical energy in a system remains constant. Take, for example, a roller coaster. At the top of a hill, the roller coaster will have the maximum gravitational potential energy, U

_{g}= mgh. Should the roller coaster be moving as well, it will also possess kinetic energy, K=The sum of these energies, K+ U, is the total mechanical energy of the roller coaster. As the roller coaster descends the hill, it will lose height and gravitational potential energy. However, the roller coaster will simultaneously gain speed and kinetic energy. During the descent, energy transforms from gravitational potential energy into kinetic energy. The force of gravity is a conservative force. When conservative forces act, the total mechanical energy of a system (the roller coaster) remains constant.

K

_{i}+ U_{i}= K_{f}+ U_{f}**Nonconservative Forces**

When nonconservative forces act, energy transfers into or out of a system. As a result, the total mechanical energy of the system is not conserved. At first glance, this seems to violate the conservation of energy. When energy is gained by the system, the energy comes from the environment. When energy is lost by the system, the energy moves to the environment. Energy is conserved when the system and environment are examined together. However, most problems deal with only a specific system. When nonconservative forces act, the energy of a system is not conserved. The transfer of energy into and out of a system is known as the work of nonconservative forces. It is equal to the change in energy of the system.

W

The most commonly encountered nonconservative force is kinetic friction, f_{nonconservative force}= ΔF_{sys }W_{nonconservative force}= E_{f}- E_{i}_{t }Kinetic friction acts on moving objects, such as the roller coaster described in the section “Conservative Forces.” When kinetic friction acts, some of the total mechanical energy of the system (roller coaster) is lost (not conserved). Kinetic friction transfers a portion of the initial energy to the environment as heat, resulting in a lower final energy for the system. As a result, the final kinetic energy and speed are less than they would have been in a frictionless environment. The decrease in kinetic energy when kinetic friction slows a moving object is referred to as

**kinetic energy lost.**As with other forms of work, the work done by kinetic friction is equal to the product of the force of kinetic friction and displacement. In addition, the work done by friction is equal to the kinetic energy lost by the system and the resulting heat transfer to the environment.

W

_{f}= - f_{k}d**Conservation of Energy When Conservative Forces Act**

**(A)**What is the total mechanical energy of the ball as measured from the ground?

**WHAT'S THE TRICK?**

All of the energy is present in the ball at the moment the ball is released. Sum the kinetic energy of the throw and the gravitational potential energy due to the height above the ground. The ground is the lowest point reached by the bail. Set the ground as zero height and zero gravitational potential energy.

**(B)**What is the total mechanical energy of the bail 2.0 meters above its release point?

**WHAT'S THE TRICK?**

The total mechanical energy is conserved and constant.

E

_{i}= E_{any point}= 125 J**(C)**What is the maximum height reached by the ball as measured from the ground?

**WHAT'S THE TRICK?**

The kinetic energy of the boy’s throw will be converted into potential energy at the top of the ball’s trajectory. In addition, when an object reaches maximum height, its vertical speed is zero.

**M**ethod

**1**:

**Energy Solution**

125 = 0 + (0.50 kg)(10 m/s)h

The height of the ledge was included in the initial energy. Therefore, the calculated final height is the height above the ground._{f }h_{f}= 25 m**M**ethod

**2**:

**Kinematics Solution**

Time is unknown. Use the kinematic equation that does not include time.

_{i}= 5 m.

**(D)**What is the impact velocity when the ball reaches the ground?

**WHAT'S THE TRICK?**

Again, the total mechanical energy remains constant. When the ball reaches the ground, the height and gravitational potential energy will be zero, mgh

_{f}= 0.

All of the ball’s initial energy will be completely converted into kinetic energy.

**Conservation of Energy and Pendulums**

**WHAT'S THE TRICK?**

In position A, the pendulum is at rest and is located at the maximum height. All of the energy is stored as gravitational potential energy. In position C, the height and gravitational potential energy are zero. Potential energy has been entirely transformed into kinetic energy. The total mechanical energy remains constant.

**Conservation of Energy and Springs**

**WHAT'S THE TRICK?**

Initially, the moving block has only kinetic energy and the spring is at rest. When the block strikes the spring, the spring compresses and the block slows. The kinetic energy of the moving block is transferred to the spring and stored as elastic potential energy. At maximum compression, all of the kinetic energy initially present has been entirely converted to elastic potential energy.

**Energy Lost by Nonconservative Forces**

**WHAT'S THE TRICK?**

If the hill were frictionless, the skier should arrive at the bottom with the kinetic energy equal to the initial potential energy. When friction acts, energy is lost from the system and transfers to the environment as heat. Energy lost due to friction is the difference between the expected and the actual kinetic energy.

K

_{lost}= (2,500 J) - (2,000 J) = 500 J
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