Physics chapter 3

Are falling objects accelerated?

Are falling objects accelerated?

before releasing an object the velocity is zero but once released the velocity has some value different from zero

If the velocity is changing there is acceleration

What was Galileo’s math do for gravitational acceleration?

To roll or slide objects down a slightly inclined plane

This allowed only a small portion of the gravitation acceleration to come into play, just that part in the direction of motion along the plane

What is a stroboscope?

A rapidly blinking light whose flashed occur at regular intervals in time

How do you find the average velocity of a falling object?

• Between the second and third flashes of a stroboscope the ball traveled a distance of 3.6 centimeters which was found by subtracting 1.2 centimeters from 4.8 centimeters. Dividing the distance by the time interval of 0.05 seconds because that is when each shot is taken yields the average size of the velocity

v = 3.6 cm/0.05s= 72 cm/s 

How do you find the value in acceleration?

• We chose two velocity values that lie on the straight line and calculate how rapidly the velocity is changing 

• The last velocity value on the chart is 464 cm/s and the second value on the chart is 72 cm/s, these two numbers are separated by 8 flashes or .40 second. The increase in velocity is found by subtracting 464 by 72 which equals 392 cm/s. 

• To find the acceleration, we divide the change in velocity by the time interval which is .4

a = 392/0.4s = 980 cm/s = 9.8 m/s^2

What is acceleration due to gravity?

The gravitation force on an object causing the natural acceleration.

This acceleration is used so often it has its own symbol

G = 9.8 m/s²

When you drop objects of different sizes and weights, do they reach the floor at the same time?

Except fort paper all object are likely to reach the floor at the same time when released simultaneously. Gravitation acceleration does not depend on the weight of the object

What is air resistance?

• impede on the falling of a feather or unfolded piece of paper because the air is pushing back onto the object making it difficult for the two objects to fall. 

• These effects produce a slower and less regular flight for light objects that have large surface area

How does velocity vary with time?

• a velocity of 30 m/s is roughly 70 MPH, so after three seconds the ball is moving quickly 

• Just after one second of the ball falling, it is moving with a downward velocity of 10 m/s which is just over 20 MPH.

How far does a ball fall at different times?

If the starting velocity is zero, we know that distance is half the acceleration multiplied by the time squared

How do you calculate the first second of fallen distance?

• During the first second of motion, the velocity of the ball increases from zero to 10 m/s. Its average velocity during that first second is 5 m/s and it travels a distance of 5 meters in that second.  

D= ½ (10 m/s^2)( 1s^2) = 5m 

What happens after the first second of motion?

• The velocity increases from 10 m/s to 20 m/s with an average velocity of 15 m/s. The ball traveled 15 meters in that second, which when added to the 5 meters in the first second gives us a total of 20 meters in two seconds. 

What is free fall?

• object is falling freely with the only force acting on it is the gravitational force

What happens when you throw a ball downward?

• The ball will reach the ground with a larger velocity.

• If the initial downward velocity is 20 m/s, after half a second it increases by 5m/s since per one second of the gravitational force 10 m/s is acting upon it. 

• After half a second it increases to 25 m/s and after one second it is 30 m/s

• We add the change in velocity to the initial velocity

• the value increases more rapidly with distance 

• formula for the distance traveled by a uniform acceleration:

d = Vo (t) + ½ (a)(t)^2

Does the effects of air resistance increase or decrease as velocity increases?

The air resistance increases the farther the object falls the greater the air resistance

How does the balls velocity change?

• When a ball is thrown up into the air at 20 m/s the gravity is the only thing that is acting on it.

• The acceleration on the ball is now negative and since the change in velocity is now downward instead of upward it is subtracted instead of added to the original velocity. 

• After one second the ball has decreased by 10 m/s. 

• So if it started at +20 m/s after one second of it going downward it is now moving with a velocity of just +10 m/s 

• after two seconds the velocity is 0 

• the sign of velocity indicates its direction 

if the velocity is zero at this point what is the value of acceleration?

It is not 0, it is -10 m/s²

The gravitational acceleration is constant and does not change

What if the acceleration was 0?

That would imply that the velocity was not changing

Since the instantaneous velocity is zero at the high point of motion, it would remain zero

How high does the ball go?

• the larger the initial velocity the greater the time to reach the high point. 

• When in its top height the ball is moving more slowly near the top of its flight than it is at lower points. 

• the time the ball takes to fall back to its starting point from the high point is equal to the time it takes to reach the high point in the first place

• It takes two seconds to reach the high point and another two seconds to return to the starting point. 

What does real path or trajectory look like?

• the ball is thrown horizontally 

• Two different things: the ball is accelerating downward under the influence of gravity and the ball is also moving sideways with an approximately constant horizontal velocity 

• the acceleration of the horizontal motion is zero 

• in each time interval the ball falls a greater distance than in the time interval before, because the vertical velocity increases with time.

• If the initial horizontal velocity is small the ball does not travel very far horizontally. Its trajectory will be its smallest starting velocity 

What determined the time of flight?

• if a ball is rolled with a low trajectory and another ball is rolled with a medium trajectory and another ball is rolled a high trajectory each ball will hit the ground roughly at the same time. 

• The reason of this is they are all accelerating at the same 9.8 m/s^2

• the horizontal distance traveled is affected by two factors: the time of flight and initial velocity 

What is the formula for direction vertically?

dvertically = ½ (a)(t)^2

What is the formula for direction horizontally?

dhorizontal = Vo(t) 

Will a bullet hit the center of a target if it shot direction at the target in a horizontal direction?

• No, it will strike the target below the center.

• For longer distances you must aim high 

• for shorter distances you must aim a little low 

• The projectile hits below where it was aimed by an amount equal to the verticals distance the target drops, because acceleration of gravity has the same effect on both the projectile and the target. 

what is the flight of the football?

• When a football is thrown the vertical component decreases because of the constant downward gravitational acceleration.

• At the high point, this vertical component of the velocity is zero, just as it is for a ball to be thrown straight upward.

How can I hit my target when throwing a ball?

• initial velocity, which is determined by how hard i throw the ball

• The launch angle which can be varied by different circumstances