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Eva8 [605]
2 years ago
8

Learning Goal: To introduce the idea of physical dimensions and to learn how to find them.Physical quantities are generally not

purely numerical: They have a particular dimension or combination of dimensions associated with them. Thus, your height is not 74, but rather 74 inches, often expressed as 6 feet 2 inches. Although feet and inches are different units they have the same dimension--length. Find the dimensions [V] of volume. Find the dimensions [v] of speed.Express your answer as powers of length ( l), mass ( m), and time ( t)
Physics
1 answer:
Ne4ueva [31]2 years ago
4 0

Answer:

volume : {l}^3

speed: (l)^1*(t)^-1

Explanation:

Volume is a measure of 3 dimensional space. It is expressed with 3 orthogonal lengths. The volume of a box would be the product of it's height, width and length. These 3 are longitudes that can be expressed in meters, feet, inches, etc. Because these are 3 longitudes multiplied the result will be a cubic longitude (l)^3.

A more general method for finding a volume is to use integral calculus:

V = \int\int\int{x} * {y} * {z} * dx * dy * dz

This is for Cartesian coordinates. Cylindrical and spherical coordinates can also be used.

Speed is defined as the rate of change in position respect of time:

vx = \frac{\delta x}{\delta t}

For movement in one dimension.

For movement in 3 dimensions you calculate the speed component of each space direction and express them as components of a speed vector:

\v{v} = \frac{\delta x}{\delta t}  \hat{i} + \frac{\delta y}{\delta t}  \hat{j} + \frac{\delta z}{\delta t}  \hat{k}

This is a vector of velocity components, each one is expressed as a division of a longitude over a time, so speed components have dimensions of (l)^1*(t)^-1

The speed vector has a magnitude that is obtained with the Pitagoras theorem:

v = \sqrt{vx^{2} + vy^{2} + vz^{2}}

Since each component is squared, added together and then the square root is taken this magnitude is also in (l)^1*(t)^-1

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A 25 kg child plays on a swing having support ropes that are 2.20 m long. A friend pulls her back until the ropes are 42◦ from t
Semmy [17]

Answer:

A) P.E = 138.44 J

B) The velocity of swing at bottom, v = 3.33 m/s

C) The work done, W = -138.44 J

Explanation:

Given,

The mass of the child, m = 25 Kg

The length of the swing rope, L = 2.2 m

The angle of the swing to the vertical position, ∅ = 42°

A) The potential energy at the initial position ∅ = 42° is given by the relation

                                P.E = mgh joule

Considering h  = 0 for the vertical position

The h at ∅ = 42° is  h = L (1 - cos∅)

                               P.E = mgL (1 - cos∅)

Substituting the given values in the above equation

                               P.E = 25 x 9.8 x 2.2 (1 - cos42°)

                                      = 138.44 J

The potential energy for the child just as she is released, compared to the potential energy at the bottom of the swing is, P.E = 138.44 J

B) The velocity of the swing at the bottom.

At bottom of the swing the P.E is completely transformed into the K.E

                  ∴                 K.E = P.E

                                     1/2 mv² = 138.44

                                     1/2 x 25 x v² 138.44

                                            v² = 11.0752

                                             v = 3.33 m/s

The velocity of the swing at the bottom is, v = 3.33 m/s

C) The work done by the tension in the rope from initial position to the bottom

             Tension on string, T = Force acting on the swing, F

                      W=L\int\limits^0_\phi{F} \, d \phi

                             =L\int\limits^0_\phi{mg.sin \phi} \, d \phi

                            = -Lmg[cos\phi]_{42}^{0}

                            = - 2.2 x 25 x 9.8 [cos0 - cos 42°]

                            = - 138.44 J

The negative sign in the in energy is that the work done is towards the gravitational force of attraction.

The work done by the tension in the ropes as the child swings from the initial position to the bottom of the swing, W = - 138.44 J

3 0
3 years ago
Blocks A and B are identical metal blocks. Initially block A is neutral, and block B has a net charge of 7.0 nC. Using insulatin
maxonik [38]

Answer:

Block A will have a final charge of 3.5nC.

Explanation:

This is because at the point of contact with Block B, which is electrically positive, the electrons in Block A will be attracted to the excess 'unpaired' protons in block B. Hence, the electrons will flow into Block B causing unpaired protons to remain in Block A.

This process is called Charging by Conduction.

This charging process will continue until the charges are evenly distributed between both objects.

In case you're wondering, "<em>how's all this possible within a few seconds</em>?", remember that electrons travel very fast and so, this process is a rather rapid one.

6 0
3 years ago
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9. What do people playing pool use to determine their shots?
jek_recluse [69]
Angles, they line up their pool que with the pocket and make the shot
7 0
2 years ago
Imagine Two Artificial Satellites Orbiting Earth At The Same Distance. One Satellite Has A Greater Mass Than The Other One? Whic
Bad White [126]

After reading this whole question, I feel like I've already
earned 5 points !

-- Two satellites at the same distance, different masses:

The forces of gravity between two objects are directly
proportional to the product of the objects' masses.  In
other words, the gravitational forces between the Earth
and an object on its surface are proportional to the mass of
the object.  In other words, people with more mass weigh more
on the Earth, and the Earth weighs more on them. 

If the satellites are both at the same distance from Earth,
then the Earth pulls on the one with more mass with greater
force, and also the one with more mass pulls on the Earth
with greater force.

-- Two satellites with the same mass, at different distances:

The forces of gravity between two objects are inversely
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In other words, the gravitational forces between the Earth
and an object are inversely proportional to the square of
the distance between the object and the center of the Earth. 

If the satellites both have the same mass, then the Earth
pulls on the nearer one with greater force, and also the
nearer one pulls on the Earth with greater force.

-- Resistor in a circuit when the voltage changes:

The resistance depends on how the resistor was manufactured. 
Its resistance is marked on it, and doesn't change.  It remains
the same whether the voltage changes, the current changes,
the time of day changes, the cost of oil changes, etc.

If you increase the voltage in the circuit where that resistor is
installed, the current through the resistor increases.  If the current
remains constant, then you can be sure that somebody snuck over
to your circuit when you weren't looking, and they either installed
another resistor in series with the original one to make the total
resistance bigger, or else they snipped the original one out of the
circuit and quickly connected one with more resistance in its place.

6 0
3 years ago
Inertia is the property that every material object has that causes objects to resist changes in its state of motion
jonny [76]
True :) good luck on your quiz
3 0
2 years ago
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