Lecture 16: Scalar Product and Work

A x B = A(Bcosθ)

Vector Projections as “Shadows”

A x B = B(Acosθ)

Vector Projections as “Shadows”

A x B = AB(1)

Special Cases: A and B are parallel

A x B = 0

Special Cases: A and B are perpendicular

A x B = -AB

Special Cases: A and B are anti-parallel

zero

What if the given vectors A and B are in component form? If we calculate A x B in this form, only terms with (i,j,k) will survive while others are ________.

A x B = AxBx + AyBy + AzBz

Given two vectors A and B in their component form, their scalar or dot product is given by?

Perpendicular

Unit vectors i, j, and k are mutually _____?

A = 4cos(53)i + 4sin(53)j

Component form of A = 4, 53 degrees.

B = 5cos(130)i + 5sin(130)j

Component form of B = 5, 130 degrees.

use inverse cos-1 and divide the components by the AB.

How do you find the angle θ between two vectors?

zero

What is the scalar product if both X,Y are multiplied to each other but in opposite directions?

No work is done if there is no displacement

Does applying a force always results to a change in the motion of an object?

W = F x s x cosθ

What is the formula of work?

Joule

What is the unit of work?

tail-tail

Where angle θ between F and s is ________? (ie. tail-head)

-15.0 [J]

A painting is moved from point A to point B at a distance of 10.0 [m] while an external constant force of 3.00 [N] is applied to it. If the angle between the external force and the displacement is 120°, what is the work done on the painting by the external force?

Work

___________ is defined as the transfer of energy when a constant force is applied to an object, causing it to move over a distance.

Kinetic Energy

__________ is the energy an object possesses due to its motion. Its unit is [J]

Kinetic Energy

______________ is the energy an object possesses due to its motion. It reflects the work needed to accelerate the object from rest to its current velocity.

speed

Work is related to the change in _______ of an object. If an object is moving, it is capable of doing work.

Potential Energy

_________ is the energy stored in an object due to its position, configuration, or condition. It represents the energy an object has because of its potential to do work in the future, based on forces acting on it.

Potential Energy

In simple terms, it's like storing energy for later use. The higher or more stretched something is, the more __________ it has.

Comparison of Kinetic and Potential Energy

Potential energy is like a battery that stores energy until you use it, while kinetic energy is like using that battery to make something happen. When the ball is up high, it has potential energy. When you drop it, that potential energy turns into kinetic energy as it falls.

Scalars

Work, Kinetic Energy, and Potential Energy are classified as ________.

Use component method and no need for angle.

In a helpful mood, Steve pushes a second stalled car with a steady force of. The displacement of the car is S = 14m(i) + 11m (j)

Calculate work done by the vertical forces, friction, tractor and add for the total work.

A farmer hitches her tractor to a sled loaded with firewood and pulls it a distance of 20 m along level ground. The total weight of sled and load is 14,700 N. The tractor exerts a constant 5000-N force at an angle of 36.9° above the horizontal. A 3500-N friction force opposes the sled’s motion. Find the work done by each force acting on the sled and the total work done by all the forces.