MEDI 11002 Lecture Notes - Lecture 1: Net Force, Potential Energy, Clothes Dryer

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pinkfrog396

26 May 2018

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ANALYSING MOTION

Vectors and scalars

- A scalar quantity is fully described by magnitude only

- A vector quantity can only be fully described by giving both magnitude and

direction

o Vector addition is represented by arrows whose lengths represent the

magnitude and arrowheads represent direction

o Vectors are added geometrically. The resultant is the vector which begins at

the tail of the first vector and ends at the arrowhead of the second.

o They have a horizontal and vertical component

Describing motion

- Displacement – distance moved in a particular direction (as measured in a

direct line from the origin)

- Distance – how far a body has travelled, irrespective of direction (displacement

in these cases could be zero)

- Speed – the rate of change of position

- Velocity – the rate of change of the position in a particular direction

- Acceleration – the rate of change of velocity in a particular direction

Calculating speed, velocity and acceleration

- The average speed provides and overall description of the motion and does not

indicated variations of speed that may have occurred during time under

consideration

   



- Instantaneous speed is the actual speed at a particular moment.

   

 

o *When the time interval tends to zero

- Average speed compared to average velocity:

   



   



- Acceleration – change in the velocity; is given by:

   



Measured in ms-2

    



o Instantaneous acceleration:

   

   

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Equations of motion:

Graphical analysis of motion

1. Displacement-time graph – slope of the graph indicates velocity

2. Velocity-time graph – slope of the graph indicates acceleration; area under the

graph indicates displacement

Newton’s laws of motion and momentum

- Law 1 – a body continues in its state of rest, or of uniform motion in a straight

line, unless acted upon by an external unbalanced force

- Law 2 – the rate of change of the momentum of a body is proportional to the

applied force and occurs in the direction of that force

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Document Summary

A scalar quantity is fully described by magnitude only. A vector quantity can only be fully described by giving both magnitude and direction: vector addition is represented by arrows whose lengths represent the magnitude and arrowheads represent direction, vectors are added geometrically. The resultant is the vector which begins at the tail of the first vector and ends at the arrowhead of the second: they have a horizontal and vertical component. Displacement distance moved in a particular direction (as measured in a direct line from the origin) Distance how far a body has travelled, irrespective of direction (displacement in these cases could be zero) Speed the rate of change of position. Velocity the rate of change of the position in a particular direction. Acceleration the rate of change of velocity in a particular direction. The average speed provides and overall description of the motion and does not indicated variations of speed that may have occurred during time under consideration.

Related Questions

1. What is the difference between speed and velocity?

a. Speed is an average quantity while velocity is not.

b. Velocity contains information about the direction of motion while speed does not.

c. Speed is measured in mph, while velocity is measure in m/s.

d. The concept of speed applies only to objects that are neither. speeding up or slowing down, while velocity applies to every kind of motion.

e. Speed is used to measure how fast an object is moving in a straight line, while velocity is used for objects moving along curved paths.

2. The quantity 2.67 x 10³ has how many significant figures?

3. If Libby walks 100 m to the right, then 200 m to the left, her net displacement vector points

a. to the right.

b. to the left.

c. has zero length.

d. cannot tell without more information.

4. Velocity vectors point

a. in the same direction as displacement vectors.

b. in the opposite direction as displacement vectors.

c. perpendicular to displacement vectors.

d. in the same direction as acceleration vectors.

e. velocity is not represented by a vector.

chocolatemouse942

An object moves clockwise with decreasing speed around an oval track. The velocity vectors at points G and H arc shown.

a. In the space at right, copy the velocity vectors and . From these vectors, determine the change in velocity vector .

b. If point H were chosen to lie closer to point G, describe how would change (direction and magnitude).

c. Describe how you would determine the acceleration (direction and magnitude) at point

G. In the space at right, indicate the direction of the acceleration of the object at point G.

d. Copy and (placed "tail-to-tail") in the space at right. How does the angle between the acceleration and velocity vectors compare to 900? (i.e., Is the angle greater than, less than, or equal to 90°?)

Generalize your results above and from tutorial to answer the following question:

For an object moving along a curved trajectory, how does the angle between the acceleration and velocity vectors compare to 90° if the object moves with (i) constant speed, (ii) increasing speed, and (iii) decreasing speed?