Chapter 5 Work and Energy

Chapter 5 Work and Energy Section 1

Work • The product of the force on an object and the distance through which the object is moved • Measured in joules(J) • Joule = N x m

Work (cont’d) • Equation: W = Force x distance • Work is done only when components of a force are parallel to a displacement • If the force is at an angle to the displacement use the equation: W= FdcosΘ

Example A person lifts a 4.5 kg block a vertical distance of 1.2 m. Determine the work done by the person.

Example When catching a baseball, a catcher’s glove moves by 10 cm along the line of motion of the ball. If the baseball exerts a force of 475 N on the glove, how much work is done by the ball?

Example • How much work is done on a vacuum cleaner pulled 3.0 m by a force of 50.0 N at an angle of 30.0° above the horizontal?

Kinetic Energy • The energy of an object that is due to the object’s motion • Measured in joules (J) • Kinetic Energy= ½ x mass x (velocity)²

Example Calculate the speed of an 8.0x10⁴ kg airliner with a kinetic energy of 1.1x10⁹ J.

Example Two 3.0 g bullets are fired with speeds of 40.0 m/s and 80.0 m/s, respectively. What are their kinetic energies? Which bullet has more kinetic energy?

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 • Equation: • Net Work = ΔKE

Example 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?

Potential Energy • Any object that is at rest has this • SI unit: Joule, J

Gravitational Potential Energy • The energy associated with an object due to the object’s position relative to gravity • PEg=mass X acceleration due to gravity X height

Example A spoon is raised 21.0 cm above a table. If the spoon and its contents have a mass of 30.0 g, what is the gravitational potential energy associated with the spoon at that height relative to the surface of the table?

Elastic Potential Energy • The energy available for use when a deformed elastic object returns to its original configuration • Ep= ½ X spring constant X (distance compressed or stretched)²

Spring Constant • Represented by “k” • Is also called the force constant

Example 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.

Example 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?

Chemical Energy • There is also chemical potential energy • This deals with the energy found in the food you eat • In one food calorie there are 4.186 J of chemical potential energy

Mechanical Energy • The sum of kinetic energy and all forms of potential energy • Mechanical Energy (ME) = Kinetic Energy (KE) + Potential Energy (PE) • ME = KE + ∑PE

Conservation of Energy • Energy cannot be created or destroyed. It can be transformed from one form into another, but the total amount of energy never changes. • Conservation of Mechanical Energy • MEi= MEf

Conservation of Energy • MEi = MEf (Equation for conservation of mechanical energy) • ME= KE + PE (Equation for mechanical energy) • KE= ½ mV² (Equation for Kinetic Energy) • PE = mgh (Equation for Potential Energy) • Therefore; ½ mVi² + mghi = ½ mVf² + mghf

Example Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg.

Example A 755 N diver drops from a board 10.0 m above the water’s surface. Find the diver’s speed 5.00 m above the water’s surface. Then find the diver’s speed just before striking the water.

Power • Measures the rate at which work is done or energy is transformed • Unit: watt, W • P= WWork Δt Time interval

Example What is the average power produced by a steam engine that does 6.8 J of work in 3.6 seconds?

Power cont’d • Equation: P= FV  Power = force X speed

Example Given: m= 19 kg V= 2.2 m/s Solve for power.

Example A motor-driven winch pulls a 50.0 kg student 5.00 m up the rope at a constant speed of 1.25 m/s. How much power does the motor use in raising the student? How much work does the motor do on the student?

Chapter 5 Work and Energy