In: Physics

A vector has components (4,2). When the vector is multiplied by the scalar 9, how does its magnitude and direction change?

Let a vector be

The magnitude of this vector is given by,

And its direction is given by,

The components of the given vector is (4,2). So the vector is given by,

So the magnitude of this vector is

And its direction is given by,

Its direction is 26.56 from the positive x-axis.

When this vector is multiplies by a scalar, the new vector is,

The magnitude of this vector is

And its direction is given by,

Its direction is 26.56 from the positive x-axis.

So when the vector was multiplied with a scalar, its magnitude changed but direction didn't change.

The 500-N force F is applied to the vertical pole as shown1. Determine the scalar components of the force vector F along the x'- and y'-axes. 2. Determine the scalar components of F along the x- and y'-axes.

(a) State Newton’s law of gravity in scalar form and vector
form.
(b) State how potential energy and forces in 1D are related and use
this to determine an expression for the gravitational potential
energy, choosing an appropriate zero-point.
(c) A thin, 1D homogeneous rod of material has a mass M and length
L. The rod is bent into a semi-circle. Determine an expression for
the strength of the gravitational ﬁeld at the centre of curvature
of the circular arc.

Identify each of the
following quantities as a vector or a scalar quantity. Select the
appropriate term from the dropdown beside each sentence.
700 J of kinetic
energy.
Answer 1Choose...VectorScalar
A distance of 38
m.
Answer 2Choose...VectorScalar
A distance of 60 miles
due north.
Answer 3Choose...VectorScalar
A temperature of 452
oC.
Answer 4Choose...VectorScalar
An acceleration of 80
m s-2 towards the east.
Answer 5Choose...VectorScalar
A tensile force of 600
N.
Answer 6Choose...VectorScalar
A speed of 50 m
s-1 at a...

Consider the retarded scalar and vector potentials. Show that
they satisfy the Lorentz gauge.

Essay
The ‘valentine
vector’ says,
“I was only
a scalar
until you
came along
and gave me
direction.”
What is your
scientific insight
in this statement?

a) show that the vector field F= <siny, xcosy, -sinz> is
conservative by finding a scalar f such that ∇f=F.
b) use this fact to ecaluate ∫C F•dr along the given curve C
where C is the line segment from (0,0,0) to (4, π/2, π/2).

-----Problem below-----
Using the Lorenz gauge calculate the scalar and vector
potentials generated by a point charge moving along trajectory r_0
(t) and find electric and magnetic field generated by this
particle.

Find the tangential and normal components of the acceleration
vector. ? (?) = ? ? ?̂+ √2 ? ?̂+ ? −??̂

2. Fill out the quantity chart.
Definition
Quantity
Unit
Scalar or Vector?
Force through a displacement.
The gravitational force Earth exerts on an object.
Change in position.
The combination of on object’s mass and velocity.
The ability to do work.
Speed and direction.
How fast an object changes how fast it’s going.
The force perpendicular to surface of contact.
The rate at which work is done.
A force parallel to the surface of contact opposing motion.
The amount of matter...

How does Charon define the components of medicine?

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