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Falling Objects and Projectile Motion. Chapter 3. Acceleration Due to Gravity. What happens if we drop an object? Does the object accelerate or fall with a constant speed? Do two objects behave differently if they have: different masses? different shapes?. Measuring Gravity Acceleration.

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acceleration due to gravity
Acceleration Due to Gravity
  • What happens if we drop an object?
  • Does the object accelerate or fall with a constant speed?
  • Do two objects behave differently if they have:
    • different masses?
    • different shapes?
measuring gravity acceleration
Measuring Gravity Acceleration
  • Galileo was the first one to accurately measure the acceleration due to gravity.
    • To measure this acceleration at that time, the action needs to be slowed down.
  • By rolling objects down an inclined plane, Galileo was able to establish that the gravitational accelerationis uniform, or constant with time.
measuring gravity acceleration4
Measuring Gravity Acceleration

Calculate the

acceleration due to the

gravity from the graph (g)

slide5
The diagram shows the positions at 0.10-sec intervals of a ball moving left to right. Is the ballaccelerated?

Example (Q2p54)

slide6
The diagram shows the positions at 0.05-sec intervals of two balls moving left to right. Are either or both of these balls accelerated?

Example (Q3 p54)

gravitational acceleration g
Gravitational Acceleration (g)

Aristotle’s and Galileo’s different ideas

The gravitational acceleration for objects near the surface of the Earth is a constant and has the value of 9.8 m/s2. It has the same value for objects with different weight and shape.

tracking a falling object
Tracking a Falling Object
  • Starting from rest, how does the velocity vary with time? (t=0.5 s, 1s, …)
  • How far does the ball fall in different times?
    • Assuming air resistance is negligible. The ball accelerates at 9.8 m/s2 ≈ 10 m/s2.
tracking a falling object9
Tracking a Falling Object
  • 10 m/s > 20 MPH
  • 30 m/s ≈ 70 MPH
throwing a ball downward
Throwing a ball downward
  • Ball is dropped:
  • Ball is thrown down:

Sample Exercise: A ball is throwing

down with an initial velocity of 20m/s. Find (a) the velocity and (b) the distance traveled at 1-s time intervals for the first 2s of motion

throwing a ball upward
Throwing a Ball Upward
  • The importance is that now the acceleration and the initial velocity is in the opposite direction.
  • What if the ball is thrown upward?

A ball is thrown upward with an

initial velocity of 20m/s, find its

velocity and height in the first four

Seconds. How high can the ball go?

examples q8 p54
Examples: Q8 (p54)
  • A rock is dropped from the top of a diving platform into the swimming pool below. Will the distance traveled by the rock in the 0.1 second interval near the top of its flight be the same as the distance covered in the 0.1 second interval just before it hits the water? Explain.
examples q9 p54
Examples: Q9(p54)
  • The graph shows the velocity plotted against time for a certain falling object. Is the acceleration of this object constant?
examples q10 p54
Examples: Q10 (p54)
  • A ball is thrown downward with a large starting velocity.
  • Will this ball reach the ground sooner than one that is just dropped at the same time from the same height?
  • Will the ball accelerate more rapidly than one that is dropped with no initial velocity?
examples
Examples
  • Q11 (p54) A ball thrown upward moves initially with a decreasing velocity.
  • What are the directions of the velocity and the acceleration vectors during this part of motion?
  • Does the acceleration decrease also?

Q 14. A ball is thrown straight upward. At the very top of its flight, the velocity of the ball is zero. Is its acceleration also zero?

examples e7 9 p55 56
Examples: E7-9 (p55-56)
  • A ball is thrown upward with an initial velocity of 15m/s. Using the approximate value of g=10 m/s/s, what are the magnitude and the direction of the ball’s velocity 1 s and 2 s after it is thrown?
  • How high above the throwing point is the ball in above question 1 s and 2 s after it is thrown?
  • At what time the ball will reach its highest point and what is that height?
projectile motion
Projectile Motion
  • Examples:

Ball running off the table

Firing a cannon

Shooting a basket ball

- an object with an initial velocity moving in the air with only the gravitational force acting on it

What does the trajectory look like? (A trajectory of a moving object is its actual moving path).

slide20

Projectile Motion

Which of these balls would hit the floor first if all three left the tabletop at the same time? Which will hit the floor with the biggest distance from the table?

  • Trajectories of a ball with three different initial velocities rolling off a table.
projectile motion21
Projectile Motion
  • Principles to treat project motion:

(1) First separate the motion in vertical and horizontal directions and threat them respectively

    • Horizontally it is a motion at a constant speed
    • Vertically it accelerates downward under the influence of gravity.

(2) The real trajectory of the object is the combination of the vertical and the horizontal motion.

example box 3 4 p 48
Example (Box 3.4 p 48)

A ball rolls off a tabletop with an initial velocity of 3 m/s. If the table is 1.25 m above the floor,

  • How long does it take for the ball to hit the floor?
  • How far does the ball travel horizontally?

Q: What determines the time of flight?

example p56
Example (p56]

E 12. A ball rolls off of a shelf with a horizontal velocity of 6 m/s. At what horizontal distance from the edge of the shelf does the ball land if it takes 0.5 s to reach the floor?

E14. A ball rolls off of a table with a horizontal velocity of 5 m/s. If it takes 0.6 s for it to reach the floor:

a. What is the vertical component of the ball’s velocity just before it hits the floor?

b. What is the horizontal component of the ball’s velocity just before it hits the floor?

hitting a target shooting a rifle
Hitting a Target (Shooting a rifle)
  • If the rifle is fired directly at the target in a horizontal direction, will the bullet hit the center of the target?
  • Does the bullet fall during its flight?
  • Example (E11, P56). A bullet is fired horizontally with an initial velocity of 900m/s at a target located 150 m from the rifle .
  • How much time is required for the bullet to reach the target?
  • Using the approximate value of g=10 m/s/s. How far does the bullet fall in this time? 
hitting a target throwing a ball and firing a cannon
Hitting a Target (throwing a ball and firing a cannon)
  • The trajectory depends on the initial velocity and the launch angle.
  • The greatest distance is achieved using an angle close to 45° if the effects of air resistance are negligible.
which of the two trajectories shown will result in a longer time for the ball to reach home plate
Which of the two trajectories shown will result in a longer time for the ball to reach home plate?

Example Q23 (p55)

example p5628
Example (p56]

E 16. A projectile is fired at an angle such that the vertical component of its velocity and the horizontal component of its velocity are both equal to 30m/s.

  • Using the approximate value of g=10m/s/s, how long does it take for the ball to reach its highest point?
  • What horizontal distance does the ball travel in this time?