PHYS1006 Lecture Notes - Lecture 2: 8 Seconds, Usain Bolt, Scientific Notation

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25 Jun 2018

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Chapter 2 Kinematics – Vectors and Projectile Motion

Mechanics: branch of physics dealing with motion of objects and the forces that cause the motion to

change.

Kinematics: Describes how objects move.

Dynamics: Describes why objects move.

Position

Is specified with respect to a reference point.

Needs a: Reference point

Direction

Distance

For example:

Where is the city of Perth?

The city of Perth is located 7km north of Curtin University.

On paper, we draw a coordinate system to give the position of places or points.

Rectangular coordinate system

Distance and displacement

For example:

A person starts at point x1 = 10m and walks to the point x2 = 30m as shown.

What is the total distance travelled?

Distance is a scalar quantity – the total path length travelled.

Distance = 30 – 10

= 20m (no direction required)

What is the total displacement?

Displacement is a vector quantity – the change in the position of an object.

Change in x: x

x = x final position – x initial position

x = 30 – 10

x = 20 metres

towards + x direction?

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Example 2

A person walks 70 m east and then turns around and walks back a distance of 30m.

If the walk took 70s, what is the:

a) Average speed?

Average speed =

Average speed = 1.4 m/s

b) Average velocity?

Average velocity =

Average velocity = 0.57 m/s towards + x direction

Review of Pythagoras

If two sides of a right-angled triangle are known we can find the 3rd side using Pythagoras’ Theorem.

c2 = a2 + b2

c =

Example 1

If a = 3m and b = 4m, what is the value of c and angle ?

c =

c = 5

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Document Summary

Chapter 2 kinematics vectors and projectile motion. Mechanics: branch of physics dealing with motion of objects and the forces that cause the motion to change. Is specified with respect to a reference point. The city of perth is located 7km north of curtin university. On paper, we draw a coordinate system to give the position of places or points. A person starts at point x1 = 10m and walks to the point x2 = 30m as shown. Distance is a scalar quantity the total path length travelled. Displacement is a vector quantity the change in the position of an object. X = x final position x initial position. A person walks 70 m east and then turns around and walks back a distance of 30m. Average velocity = 0. 57 m/s towards + x direction. If two sides of a right-angled triangle are known we can find the 3 rd side using pythagoras" theorem. c2 = a2 + b2 c =

Related Questions

Good Vibes: Introduction to Oscillations

The conditions that lead to simple harmonic motion are as follows:

There must be a position of stable equilibrium.

There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. Mathematically, the restoring force F⃗ is given by ⃗, where is the displacement from equilibrium and k is a constant that depends on the properties of the oscillating system.

The resistive forces in the system must be reasonably small.

Consider a block of mass m attached to a spring with force constant k, as shown in the figure(Figure 1) . The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x=0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations.

Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.

Part A

After the block is released from x=A, it will

(a) remain at rest

(b) move to the left until it reaches equilibrium and stop there.

(d) move to the left until it reaches x=−A and then begin to move to the right.

The time it takes the block to complete one cycle is called the period. Usually, the period is denoted T and is measured in seconds.

The frequency, denoted f, is the number of cycles that are completed per unit of time: f=1/T. In SI units, f is measured in inverse seconds, or hertz (Hz).

Part B

If the period is doubled, the frequency is

(a) unchanged

(b) doubled

Part C

An oscillating object takes 0.10 s to complete one cycle; that is, its period is 0.10 s. What is its frequency f?

Express your answer in hertz.

Part D

If the frequency is 40 Hz, what is the period T?

Express your answer in seconds.

The following questions refer to the figure (Figure 2) that graphically depicts the oscillations of the block on the spring.

Note that the vertical axis represents the x-coordinate of the oscillating object, and the horizontal axis represents time.

Part E

Which points on the x-axis are located at a distance A from the equilibrium position?

(a) R only

(b) Q only

Part F

Suppose that the period is T. Which of the following points on the t-axis are separated by the time interval T?

(a) K and L

(b) K and M

(d) L and N

(e) M and P

Now assume for the remaining Parts G - J, that the x coordinate of point R is 0.12 m and the t coordinate of point K is 0.0050 s.

Part G

What is the period T?

Express your answer in seconds.

Part H

How much time t does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement?

Express your answer in seconds.

Part I

What distance d does the object cover during one period of oscillation?

Express your answer in meters.

Part J

What distance d does the object cover between the moments labeled K and N on the graph?

Express your answer in meters.

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PHYS1006 Lecture Notes - Lecture 2: 8 Seconds, Usain Bolt, Scientific Notation

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