Chapter 3
Falling Objects and
Projectile Motion
Gravity influences motion in a particular way.
How does a dropped object behave?
!Does the object accelerate, or is the speed constant?
!Do two objects behave differently if they have:
!different masses?
!different shapes?
Acceleration Due to
Gravity
" Earth exerts a gravitational force on objects
that is attractive (towards Earth’s surface).
" Near Earth’s surface, this force produces a constant acceleration downward.
#
#
#
To measure this acceleration, we need to slow down the action.
Galileo was the first to accurately measure this acceleration due to gravity.
By rolling objects down an inclined plane, he slowed the motion enough to establish that
…show more content…
The velocity-versus-time graph for a certain falling object is shown.
Is the acceleration of this object constant? a)
b)
c)
Yes.
No.
Impossible to tell from this graph.
Constant acceleration would require the v vs. t curve to be a straight line. This graph is curving upward, so the slope
(and the acceleration) is increasing. Throwing a ball downward " Let the ball be thrown downward
instead of being dropped.
It will have a starting velocity different from zero. # It will reach the ground more rapidly.
# It will have a larger velocity when it reaches the ground. v = v 0 + at
#
1 2 d = v 0 t + at
2
Beyond Free Fall:
Throwing a Ball Upward
! What if the ball is thrown
upward?
Gravitational acceleration is always directed downward, toward the center of the Earth.
! Here, the acceleration is in the opposite direction to the original upward velocity.
!
" Let the initial velocity be 20
m/s upward.
#
#
It immediately starts experiencing a downward acceleration due to gravity, of approximately 10 m/s.
Every second, the velocity decreases by 10 m/s.
" After 2 s, the ball has reached
its highest point.
#
Its velocity changes direction, from upward to downward, passing through a value of 0 m/s. " Now, the downward
acceleration increases the downward velocity.
What is the ball’s acceleration at the top of its
ball’s acceleration (a) depends on the applied force (F) divided by the object’s mass (m) (The
Theory: During the early part of the seventeenth century, Galileo experimentally examined the concept of acceleration. One of his goals was to measure the acceleration due to gravity, or the acceleration of freely falling objects. Unfortunately, his timing devices were not precise enough to measure the free fall time directly. He decided to “dilute” gravity by using fluids, inclined planes, and pendulums.
The average distance was 1.27 meters (Data Table 1).The marble was also launched at an angle of 25 degrees and a height of 1.05 meters. The average distance was 1.46 meters (Data Table 2). The marble took .452 seconds to hit the ground (Figure 1). The marble had an average velocity of 2.82 m/s (Figure 2). A triangle was drawn with a magnitude of 2.82 m/s. The x and y components of the triangle were calculated.
Purpose: To examine the motion of a free falling object by using a picket fence dropped through a Photogate and using the slope of a velocity vs time graph to verify the acceleration of the Earth’s gravity (9.8 m/s²).
As the height of the ramp increases so will the distance the marble travels, because the marble will be going faster
The image ‘types of projectiles’ (2015) shows three types of projectiles. P1 is the projectile which has the movement only in vertical direction while P2 has more vertical and a little horizontal motion thus moving in two dimensions. P3 has both motions almost equal. Projectile has the characteristic of being under influence the force of gravity only. If the path of a moving object is affected significantly by some air resistance, the object is not a projectile any more. It is also not a projectile while at the source or when it hits something during its flight. A ball shown in the diagram below is not a projectile till the ball leaves the hands of the person dropping it or throwing it. The air resistance can be ignored at this point because the effect is not significant. It again seizes to be a projectile when it is in contact with the ground because the force of the reaction from the ground and the force of friction has come into action.
An object can be accelerating when its speed is zero, because acceleration is a change in velocity, so an object might be momentarily at rest
The purpose of this experiment was to replicate Galileo’s incline experiment and to see if the classroom experiment would produce the exact measurement for the acceleration of gravity in meters per seconds squared that Galileo produced. It was hypothesized that the solid metal ball would have an acceleration of gravity between 9.8 and 10 meters per second squared.
Our contraption is made of balloons, string, Popsicle sticks, cups, cotton, and rubber bands. In this experiment gravity, drag, and impact are demonstrated. Gravity is the force that pulls objects towards each other. This is when the egg is falling to the ground. The drag is when the object is acting is the opposite direction. This is the balloons attached to the egg which slows it down. Finally impact is the shock when to objects collide. This is why cotton balls are on the bottom to absorb the impact. These are all Newton's law of motion.
When these forces are exerted on either an object in motion or at rest, these states of motion can change. For example, when launching a projectile from the catapult, the object was initially at rest until the force exerted by the catapult arm launches the catapult into the air. While in the air, the projectile experiences another force (gravity) which causes its path of motion to change. This path of motion is called projectile motion, or the combination of horizontal and vertical motion that happens on any thrown object. Without the discovery of newton’s first law, projectile motion would have never been discovered, and accuracy would greatly decrease. This is mainly because of this combination of horizontal and vertical motion, which changes where the object will hit the target, as well as the accuracy of the object itself. As an example, take a bow and arrow. If you were to aim exactly for the bullseye on a target, you would not be able to hit it due to projectile motion, which causes the arrow to curve down at an angle before it even reaches the target. This is the same with a catapult projectile, also having this downward curve before it becomes at rest by either hitting the ground or the
The mass of a falling object does not affect its speed (disregarding air resistance) and hence at equal instants two objects of different masses should be at the same speed (Socratic, 2015). This is due to the fact that when an object’s mass is increased, its inertia (tendency to resist motion) will also increase, and hence this will cause the force of gravity on the mass to increase, as gravity does not pull objects of different masses at different rates (Education.com, 2015). Therefore, the masses fell at similar speeds, as when their mass increased, the force of gravity on the cans in turn increased to pull the masses at the same rates. The slight variation in speeds can be considered the result of air resistance. The discovery of the fact that the gravitational accelerations of the masses were somewhat similar, with a maximum variance of -1.927m/s/s, in table 2, is due to Newton’s second law of motion, which proves that different masses accelerate to the earth at the same rate. As acceleration depends on force and mass, an increase in mass has an inverse effect on its acceleration. The direct effect of the greater force on the object caused by its increased mass is offset by this inverse effect and causes objects of different masses to accelerate at the same rate of
Purpose The purpose of the experiment is to find the existing relationship between the angle of inclination of a straight ramp, and the acceleration of a ball on the ramp. Background The angle of inclination, is the angle between the floor, and the elevated ramp.
The aim of the investigation was to determine the bounce efficiency of a tennis ball at varying heights and it was hypothesised that as the drop height was increased, so too will the bounce height due to the extra gravitational potential energy being added with an increase of drop height. The findings indicated subtle changes occur in the bounce efficiency of the tennis ball from 91%, but with an overall decline in the chosen linear trend line. The results of the experiment support the hypothesis that as drop height increases, so too will the bounce height due to an increase in gravitational potential energy, however the bounce efficiency remained relatively
Gravity is responsible for a number of things such as our weight, rainfall, the turning of the planets, and why objects fall. Proven already, that if an object is in free fall the only force active is gravitational force. And when force is thrown into the mix and acts on gravity it cause an object to accelerate or speed up. Hence the purpose of this lab is to prove that an object under the impact of gravity will accelerate at a constant rate. Acceleration will also be measured and compared to its actual value 9.8 m/s^2 , the value is negative because gravitational acceleration is downward and noted by as a=-g. It is predicted and expected that the outcome for this lab is that the ball free falling would have a negative velocity and then become
– vo (vf = final & vo = original) • a= = t t • Units of acceleration = (m/s)/s = m/s2 • In this course we will limit ourselves to situations with constant acceleration.