principles of technology waxahachie high school

Principles of TechnologyWaxahachie High School

Principles of TechnologyWaxahachie High School

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Mechanical Systems

PIC Chapter 3.1

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Mechanical Systems

PIC Chapter 3.1

PT TEKS PT TEKS

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Objectives:

Define speed, velocity, and acceleration Explain the difference between speed and velocity Explain the difference between velocity and acceleration Use speed, velocity, and acceleration to solve problems involving linear

motion Define angular speed and angular acceleration Use angular speed and angular acceleration to solve problems

involving rotational motion

Objectives:

Define speed, velocity, and acceleration Explain the difference between speed and velocity Explain the difference between velocity and acceleration Use speed, velocity, and acceleration to solve problems involving linear

motion Define angular speed and angular acceleration Use angular speed and angular acceleration to solve problems

involving rotational motion

The speed of an object is the ratio of distance in a given time.

You can measure speed with a stop watch and a meter stick.

Speed = Distance / time

S = d/t

This equation tells us the speed if the speed is constant

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If the speed varies, than we must find the average speed.

Average speed =

change in distance / change in time

Vave = Δd / Δt

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You leave home and drive 100 miles east to your friend’s house. The trip takes 2 hours. On the return trip you drive through a rainstorm and it takes 3 hours driving the same 100 miles. Calculate the average speed driving to your friend’s house. Calculate the average speed driving from your friend’s house. Calculate the average speed for the entire trip.

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Calculate the average speed driving to your friend’s house.

Vave = Δd / Δt

Vave = 100 miles / 2 hrs

Vave = 50 miles / hr

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Calculate the average speed driving from your friend’s house.

Vave = Δd / Δt

Vave = 100 miles / 3 hrs

Vave = 33.3 miles/hr

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Calculate the average speed for the entire trip.

Vave = Δd / Δt

Vave = 200 miles / 5 hrs

Vave = 40 miles/hr

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The speed at any one instant is called the instantaneous speed.

The instantaneous speed can be found in a car with the speedometer.

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When we state the speed and direction of an object, we are stating the object’s Velocity.

Velocity tells us direction and size so it is a vector.

Speed tells us only size so it is a scalar.

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The vector that defines the distance and direction between two positions is called displacement.

Displacement is like a short cut directly from one point to another.

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Average velocity = displacement / time

V = d/t

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If you have a displacement of 145 km and your flight takes 2 hours, what is your average velocity?

v = d/t

v = 145 km / 2 hrs

v = 72.5 km/hr

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The rate of change of an object’s velocity is the acceleration. (How fast you speed up or how fast you slow down)

Acceleration is a vector.

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Average acceleration =

change in velocity / time

a = (Vf – Vi) / t

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A pilot increases the takeoff speed of an airplane from 20 ft/s to 200 ft/s in 30 seconds. What is the average acceleration?

a = (Vf – Vi) / t

a = (200 ft/s – 20 ft/s) / 30 s

a = 180 ft/s / 30 s

a = 6 ft/s2

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Speed and velocity are rates of linear motion. (in a straight line)

Angular speed is a rate of rotational motion. The symbol for angular speed is ω, the Greek letter omega.

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Angular speed =

angular displacement / time

ω = Δθ/Δt

Angle = # of turns x 2pi

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If we have a tire that rotates 30 times in 60 seconds, what is the angular speed of the tire?

ω = Δθ/Δt

θ= # of turns x 2 pi

θ = 30 x 2 pi

θ = 188.4 rad

ω = 188.4 rad / 60 s

ω = 3.14 rad / s

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Speed = radius x angular speed

v = r x ω

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A vacuum cleaner has a shaft that is 1.5 inches in diameter and turns at an angular speed of 2000 rad/s, what is the speed of the belt connected to this shaft?

ν = r x ω

radius = diameter/2

r = 1.5 / 2 = .75

v = .75 in x 2000 rad/s

v = 1500 in/s

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Change in angular speed =

angular acceleration

The angular acceleration is the ratio of the change in angular speed to the time interval.

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Angular acceleration (α - alpha) =

change in angular speed / time

α = (ωf – ωi) / t

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A car’s brake is applied to a wheel for 5 seconds, reducing the wheel’s angular speed from 220 rad/sec to 180 rad/sec. What is the angular acceleration?

α = (ωf – ωi) / t

α = (180 rad/s – 220 rad/s) / 5 s

α = -40 rad/s / 5 s

α = -8 rad/s2

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