Work, Power And Energy

**Work – **Defined as the product of a force and the displacement caused by the force. If a force acts entirely in the direction of the displacement, the entire force does work. If the force acts in a direction other than the exact direction of the displacement, use resolution of force techniques to determine the effective component. The effective component is then used to compute the work. Work is expressed in Joules (N•m). **Equation: W = F•d**

**Power **– Defined as the rate of doing work. Power is computed by dividing the total work done by the time required for the work. Power is expressed in Watts (J/s). **Equation: P = W/t.**

**Energy** - Defined as the ability to do work. There are many different types of energy such as electrical, light, magnetic, heat etc. Mechanical energy is classified as **kinetic** or **potential**.

**Conservative Verses Non-Conservative Forces: **A force for which work done does not depend on a path of motion (just initial and final position or state) is called a **conservative force**. Gravity, elastic forces, and electric forces are conservative. A force such as friction depends upon the path through which it acts and is refereed to as a **non-conservative force**.

The **energy** possessed by a body by virtue of its **position **or **state. This energy is only associated with conservative forces.**

**Gravitational PE: **This is energy, which is stored in the gravitational field of the Earth. If work is done in separating an object from a zero point (lifting it up) the energy stored in the gravitational field is equal to the work done in lifting the object. **Equation: PE _{grav} = mgh** (measured in Joules).

**Elastic PE: **This is energy, which is stored by distorting the shape of an elastic object such as a spring or a bow. The distorted **state** of the object is that aspect of the object, which contains the energy. The work done in distorting the object is equal to the energy stored in it. **Equations: PE _{elastic} = ½ks^{2} **(measured in Joules) where k is the elastic constant of the object and s is the amount of distortion or

stretch.

stretch.

**Kinetic Energy** is the **energy** possessed by a body by virtue of its **motion**.

Any moving object has kinetic energy. **Equation: KE = ½mv ^{2 }**(measured in Joules).

In a **closed system of conservative forces** (no energy input or loss), the total energy of the system remains constant.

If a system consists of a weight suspended from some height, the total energy of the system is **PE _{grav. }**If the weight is released and falls, the

If a system consists of a drawn bow and arrow, the total energy of the system is stored in the bow as **PE _{elastic.}** When the arrow is released, all of the

- A team of mules pulls with a force of 2500 N on a wagon. How much work does the team do if the wagon is pulled 1820 m?
- A 45 Kg box is lifted from the floor to the top of a shelf 1.1 m high. Compute the work done against gravity.
- A man pulls a sled by means of a rope, which makes an angle of 48° to the horizontal. If the sled is moved a total distance of 56 m, compute the work done by the man if he pulls the rope with a force of 200 N.
- A sled is pulled a distance of 185 m by means of a rope held at some angle θ measured from the horizontal. If 12000 J of work is done and the pull along the rope is 125 N, compute the value of θ.
- A crane lifts a 2250 N bucket containing 1.15 m
^{3}of sand. If the density of sand is 2000 Kg/m^{3}, and the bucket is lifted 8.4 m, compute the work done against gravity. - A 250 N weight is pushed up a 5.6 m frictionless inclined plane, which makes an angle of 35° to the horizontal. Compute the work done against gravity. Hint: find the height of the inclined plane.
- A conveyor belt lifts 56 Kg of stone up to a height of 15 m. If the machine lifts the load in 55 seconds, compute the power output of the conveyor belt in kW.
- In 35 seconds, a pump delivers 56 dm
^{3}of liquid into a tank 31 m above the reservoir. If the density of the liquid is 0.91 Kg/dm^{3}, compute the work done and the power output of the pump. - A 115 N force exerted by a rope, which makes an angle of 43° to the horizontal, pulls a sled. If the rope generates 66 W of power for 92 s, compute the distance that the sled moves as a result. Hint: find the effective component of the force first.
- A 14 m conveyor belt inclined at 35°, delivers bundles of recycled paper, which have a mass of 5.0 Kg. If the conveyor belt delivers 23 bundles per minute, compute the power output of the machine>

- The elastic force constant of a spring in a toy is 550 N/m. If the spring is compressed 1.2 cm, compute the potential energy stored in the spring.
- A total of 56 J of potential energy is stored in a spring that is stretched 4.5 cm. Compute the elastic force constant of the spring.
- A force of 125 N is used to stretch a spring 0.33 m. Compute the potential energy stored in the spring.
- A 100.0 g arrow is pulled back 30.0 cm against a bow, which has an elastic force constant of 125 N/m. If the entire potential energy stored in the bow is converted to the kinetic energy of the arrow, compute the speed of the arrow.
- A spring with a constant of 650 N/m is compressed to 5.5 cm and is used to shoot a toy dart with a mass of 56 grams straight up. Assuming that the entire potential energy in the spring is converted to kinetic energy, compute the speed of the dart upon launch.
- If all of the energy of the dart in problem 15 is converted to gravitational potential energy by the dart being fired straight up, compute the height that the dart will reach.
- A force of 56 N is used to compress a spring 2.35 cm. Compute the potential energy stored in the spring.
- If the spring in problem 17 is used to launch a 2.1 g ball straight up, compute the maximum height that the ball will reach.

- A 550 Kg roller coaster train rolls down from the top of a hill 94 m high. What is the loss of potential energy at the bottom of the hill? Assuming that all of the potential energy lost is converted to kinetic energy, compute the speed of the train.
- A roller coaster train rolls down from the top of a hill 85 m high. Assuming a 21% loss of energy to friction, what is the speed of the coaster train at the bottom of the hill?
- A 2.1 Kg weight receives 210 J of kinetic energy by a launcher, which is pointed straight up. What is the maximum height that the weight will achieve?

- A machine receives a work input of 25 J and has efficiency rating of 54%. Compute the useful work output of the machine.
- An effort of 55 N acts through a distance of 1.2 m to lift a 350 N weight straight up. Assuming that the machine is 100% efficient, compute how high the weight will be lifted by the machine.
- An effort of 545 N is exerted on the rope of a pulley system. The rope is pulled 10.0 m. If this work causes a 2520 N weight to be raised 1.50 m, compute the efficiency of the machine.
- An effort force of 56 N acts through a distance of 15 m to raise a 1120 N weight a distance of 0.525 m straight up. Compute the IMA, the AMA, and the efficiency of the machine.
- What work input is required to lift a 215 Kg mass a distance of 5.65 m using a machine that is 72.5% efficient?

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