WORK AND ENERGY

QUICK REVIEW

Kinematics DynamicsUCM and

Newton’s Law of Gravitation

• Studied motion but not cause of motion.

• Relationships between position, displacement, velocity, acceleration and time.

• Mathematical relationships

• Applied kinematics• Studied the cause

of changes in motion.

• Newton’s Laws of Motion

• Physical and mathematical relationships

• Dynamics applied further

• Constant speed, change in direction

• Universal Law of Gravity

• Forces and motion of planetary systems

ENERGY•Not easily defined

–Usually described by type of energy

• Classical Physics –Energy is the ability to do work.

–More energy = more ability to do work

• Conservation of Energy–The total amount of energy in the entire Universe is

conserved.

–Cannot be created or destroyed

–Can transfer to different types or be stored

WORK

•Work is the product of the force and displacement.

• In this equation θ is the angle between F and Δx.

• The unit would be the Newton-meter (Nm) or the Joule (J)

𝑊=𝐹 ∆𝑥𝑐𝑜𝑠 𝜃

MORE WORK

•Work is scalar – no direction in its value

• Even though your are multiplying two vectors, you get a scalar

• In maths this is called a dot product. It its one of two ways of multiplying vectors.

• A dot product aims to multiply the components of vectors that are parallel to one another!

WORK EXAMPLES

EXAMPLE• Tarzan is trying to impress Jane with his new cart. The elephant is gone for the day so while Tarzan steers, Jane pushes the cart 19 m using a force of 210 N. If Jane pushes in the direction the cart is heading, how much work will she do?

• If Tarzan weighs 600 N, how much work does he do by pushing down on the cart?

EXAMPLE• Farmer Mellyn hitches his tractor to a sled loaded with firewood and pulls it 20 m. The tractor exerts a constant force of 5000 N at an angle of 30o as shown. There is a constant force of friction of 3500 N. Find:

– the work done by friction

– the work done by the tractor

– the total work done

EXAMPLE• A block of mass 3 kg slides up an inclined plane tilted at 37o to the horizontal. There is a frictional force of 8 N. When the block has slide 3 m up the ramp, how much work had been done by:

–Gravity

–Friction

–Normal

EXAMPLE• A girl pulls a crate 10 m by applying a force of 150 N at 37o above the horizontal. The crate has a mass of 5 kg and there is a coefficient of friction of 0.3 between the crate and the floor. Determine the work done by:

– the girl.

– friction.

–weight.

–Determine the total work done.

POWER

• Power is the rate at which work is done.

• Measured in J/s or Watt (W)

• 1 hp = 746 W

• Power is not a measure of how much work you can do but how fast you can do it.

𝑃=𝑊𝑡

MORE POWA

• 𝑃=𝐹𝑣𝑐𝑜𝑠𝜃

EXAMPLE• An elevator has a mass of 600 kg. The elevator is designed to move upward at a constant speed a distance of 20 m in 16 sec. What is the minimum power rating on a motor to accomplish this task?

• If you used a 40 hp motor, how many people can be in the elevator if the average passenger mass is 65 kg?

EXAMPLE• The engine of a motorboat delivers 30 kW to the propeller while the boat is moving at 15 m/sec. What is the resistive force acting on the boat?

STAIR ACTIVITY:

•Get a half sheet of paper: 1. Convert your weight into mass (1 kg = 2.2 lbs)

2. How much work would you have to do to lift yourself up a flight of stairs 8 meters in height? Only consider vertical displacement.

3. We will go to the stairs in the cafeteria (h = 4.3 meters). Time how long it takes for you to run or walk up the stairs. Calculate your power output in hp.

THE MOST POWERFUL IN ALL OF AP PHYSICS

Will Jordan1.87 hp

Juliana Kolb0.92 hp

HORSEPOWER!

•How unemployment skyrocketed amongst horses in the 18th century.

1 calorie of heat is required to warm 1 g of water by 1°C.

1 calorie = 4.184 J1 Calorie (kcal) = 4184 J

GRAPHS •Work:

𝑊=𝐹 ∆𝑥𝑐𝑜𝑠 𝜃