Acceleration & Inclined Planes Unit 5 – Lecture 3

“change in” ∆ Greek letter Delta Always described as the final condition minus the initial condition “Change in speed” v final – v initial v f - v i

Acceleration Acceleration – the rate of change of velocity –change in velocity over a change in time a acceleration t f - t i change in time v f - v i change in velocity a = v f - v i t f - i i

Acceleration Formula a acceleration = ∆ t Change in time ∆v Change in speed a ∆v ∆ t

Acceleration – cont’d Units for acceleration: –unit of distance / [unit of time] 2 explanation: if unit for velocity: m/s if change in time measured in seconds = s –unit = (m/s)/s = m/s 2 –for every second that passes, the object will accelerate this number of meters per second

Acceleration – cont’d

Two ways to accelerate Change speed –Speed up –Slow down Change direction Remember that velocity is speed and direction Changing speed or direction is acceleration Acceleration can be negative (deceleration), depending on the change in the frame of reference

Acceleration – cont’d

1.Which has the greater acceleration, an airplane that goes from 1000 km/h to 1005 km/h in 10 s, or a skateboard that goes from 0 to 5 km/h in 1 sec? 2.What is the acceleration of a race car that whizzes past you at a constant velocity 400 km/h? 3.If you’re running at 12 m/s and you accelerate at 0.33 m/s for 6 s, how fast are you going?

Gravity Gravity – the attraction of one mass toward another –depends on the masses of each –their distance from one another

Gravity – cont’d g = acceleration due to gravity –g = 9.8 m/s 2 on earth –g will change if the object gets farther away from the center of the earth [distance change] the object’s mass changes [but not in relation to the earth]

Observed Constant Acceleration Gravity is the attraction of one mass toward any other mass. –It decreases over distance Explains why the Moon has more gravitational effect on the Earth than the Sun Here, gravity is a constant acceleration downward (toward the center of the Earth)

Practice Which of the following (if any) could not be considered an “accelerator” in an automobile: gas pedal, brake pedal, steering wheel? A sports car accelerates from 65 mph to 75 mph in 2 seconds while a minivan accelerates from 20 mph to 35 mph in 2 seconds. –which has the greater acceleration? [end]

Falling Objects

Gravity – cont’d Galileo Galilei –experimented to find out the acceleration of free-falling objects showed that free-fall was constant had difficulty showing this before using inclined planes –plane reduced force of gravity & increased distance, but with same result

Acceleration on Galileo’s Inclined Planes Galileo found greater accelerations for steeper inclines. The ball attains max acceleration when the incline is tipped vertically.

Air Resistance Air resistance – the friction of air particles on an object moving through it –accounts for varying speeds of falling objects

At a given location on the Earth and in the absence of air resistance, all objects fall with the same, constant acceleration

Recap Galileo’s Observations: –a ball rolling down an inclined plane is moving with constant acceleration – greater accelerations for steeper planes, max acceleration when incline is tipped vertically – regardless of weight and size, when air resistance is small enough to be neglected, all objects fall with the same unchanging acceleration

g Acceleration due to gravity 9.8m/s 2 On Earth, g has a value of 9.8m/s 2 g will change if: –The object gets farther from the center of the Earth –The object’s mass changes (but not in relation to the Earth)