# MOTION SUBJECT TO GRAVITATIONAL FORCE

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FREE FALL and MOTION SUBJECT TO GRAVITATIONAL FORCE PART A (50%)

1. Introduction

When air resistance is negligible, all objects dropped under the influence of gravity near Earth’s surface fall toward Earth with the same constant acceleration. We denote the magnitude of the free-fall acceleration by the symbol g. The value of g decreases with increasing altitude, and varies slightly with latitude as well. At Earth’s surface, the value of g is approximately 9.81 m/s2. In this experiment, students will determine free – fall acceleration, by measuring the time interval of the free fall and the height, from which the object is falling.

## FREE FALL and MOTION SUBJECT TO GRAVITATIONAL FORCE

Figure 1. Free Fall Apparatus

Figure 2.

Releasing the steel ball from rest

1. Objectives
• To verify the equation of motion of a free falling object (equation 2).
• To determine graphically the acceleration gdue to gravity.
1. Experimental setup:

1 Base plate

2 Stop socket

3 Ground socket

4 Start socket

5 Socket for stand rod with fixing screw

6 Contact plate

7 Stand rod with scale

8 Steel ball

9 Start fitting with release mechanism

10 Retaining lug with micro-magnet

11 Release lever

12 Clamping lever for start fitting

Figure 3.

### Free Fall apparatus

1 4-mm-socket “Start”

2 4-mm socket “Stop”

3 4-mm socket “Ground”

4 Power supply socket

5 4-digit display

Figure 4.

Motion under gravity

#### Millisecond Counter

1. Theory

If a body falls to the ground in the Earth’s gravitational field from a height h, it undergoes a constant acceleration g, as long as the speed of the fall is slow so that friction can be ignored. Such a falling motion is called free fall.

In this experiment a steel ball is suspended from a release mechanism. As soon as it is released into free fall, an electronic timer is started. After it has fallen a distance h the ball hits a target plate at the bottom which stops the time measurement at a time t.

Since the ball is not moving before it starts to fall at time its initial velocity is zero, i.e. . The origin of vertical positions will be chosen as the release point for that we have

By applying the equation of a vertical motion with constant acceleration we have:

(1)

as

The distance covered in time t is given as follows:

(2)

The velocity of the ball is linearly increasing with time as follows

(3)

1. Experimental Procedure

A – Using the Free Fall Apparatus:

1. Connect the free-fall apparatus to a timer. Make sure you keep to the color coding of the sockets.

Figure 5.

## Connecting Free-Fall apparatus to the millisecond timer

1. Set the release lever and adjust the height of fall. The height of fall can be read off the scale on the rod and is referenced to the top edge of the bore on the start fitting. The reading on the scale corresponds to the distance covered, i.e. the distance between the ball and the contact plate at the bottom.

Figure 6.

### Adjusting the height of fall

1. Place the steel ball between the contact pins from below so that it is held in place by the retaining lug when the latter is pressed down.
2. Allow the ball to fall by pushing lightly on the release lever. For optimum precision and reproducibility, the release must be operated gently and carefully. The micro-magnet moves away from the surface of the ball. The start contact opens at the instant the ball begins to fall. When the ball hits the contact plate at the bottom, the stop contact is opened briefly and the time measurement is stopped.

Figure 7.

#### Measuring the ball free falling time

B – Using the Strobe Photography technique:

Figure 8

Strobe Photography is a technique which captures several frames of a movement, and combines them into a single image.

Figure 8 is a strobe photograph of a ball moving in a straight line with constant acceleration. While the ball was moving, its image was captured ten times in one second, so the time interval between successive images is 0.10 s. The motion in this picture took place in about 1.00 s. In this short time interval, your eyes could only detect a blur. This photo shows what really happens within that time.

To study the motion of a falling object (Billiard ball) is to make and analyze a strobe photograph or a slow motion film.

The photograph shows a billiard ball being dropped in the air by a hand. As the ball moved a strobe light illuminated it at regular intervals, producing the multiple images in the single photograph.

To analyze the ball’s trajectory you will simply use a ruler to measure the position of the ball and then do some graphing.

1. Analysis/Report
2. Use the DATA TABLE 1 on Moodle and complete the graphs below.
3. Graph height versus time (10%)
4. Graph height versus time2 (2%)
5. Using the slope found above and the equation (2) in the report, calculate the acceleration g due to gravity. (3%)

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1. Consider the following strobe photograph. The photo was resized to the scale 1/9 this means you need to multiply the lengths measured directly in the photo by 9 to get the real length. The time step between 2 successive photos is 0.05s.

Using the yellow vertical line as a ruler fill in the table below. (15%)

 Photo # Time t (s) Δy (cm) Δy (m) V= Δy/Δt (m/s) 0 0 0 0 1 0.05 2 0.10 3 0.15 4 0.2 5 0.25 6 0.30 7 0.35 8 0.40 9 0.45 10 0.50
1. Using the table above complete the graph velocity versus time. (5%)
2. Using the slope found above and the equation (3) in the report, find the acceleration g due to gravity. (5%)

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1. Compare the value of g found by the 2 methods (Using the Free Fall apparatus versus using the strobe photograph) which one of the 2 methods is more accurate. (5%)

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1. Give one reason to explain the inaccuracy. (5%)

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### FREE FALL and MOTION SUBJECT TO GRAVITATIONAL FORCE PART B (50%)

1. Introduction

Recall that gravitational force is always vertical and directed toward earth’s center (downward). A system is said to be falling freely if it is released from rest and subjected dominantly to gravitational force ( ). On the other hand, a projectile is any object that has been thrown or launched, causing it to move along a curved path under the action of gravity.

If air resistance is neglected, gravitational force would be the only force acting on a freely falling object or a projectile. In the current experiment, air resistance will be neglected and factored into the experimental uncertainty. In this experiment a projectile launcher will be used to study Projectile Motion experimentally in order to better understand the kinematics and dynamics of a Projectile Motion.

Figure 1 –

### Motion subject to gravitational force

1. Objectives
• To predict the range and time of a ball launched at an angle by measuring the initial velocity first.
• To compare experimental values for time of flight and range, with values obtained using the projectile equations (equation 8 and equation 11).
1. Experimental setup:
• Mini Launcher.
• Steel Ball.
• Plastic Rod
• White and Carbon Paper
• Tape

Figure 2 –

##### Mini Launcher setup
• Meter
• Smart Timer
• Time of flight Sensor
• Ruler
1. Theory

The position vector for any moving object subject to a constant net force is:

(1)

Equation (1) gives two equations for the x and y directions as

(2)

(3)

hence

= 0 and

Substituting in equations (2) and (3), we arrive at

(4)

(5)

Recall that (gravitational acceleration).

In case of a projectile motion the components of the initial velocity of a projectile are:

= (6)

= (7)

The range for the projectile is defined as (the distance covered in the direction).

From equation (4), we have:

, (8)

hence

(9)

Another important quantity while studying the projectile motion is the time of flight Δ (the time required by the object to reach its destination). Time Δ can be determined using equation (5). Considering that , where h is the height from table to launcher (figure 2), we get Δ as:

= (10)

hence,

(11)

1. Experimental Procedure
2. Read the angle from the protractor on the mini-launcher side (figure 3) and make sure it’s at the desired value.

Figure 3 – Reading launching angle

1. Insert the ball into the launcher and push it using a rod (figure 4) and not your finger to avoid it getting stuck! Note that the launcher has 3 speeds, so expect to hear 3 clicks if you push the ball all the way in. Make sure you push to the desired speed.

Figure 4 –

##### Setting launch speed
1. Measure the distance between the two gates fixed on the launcher (figure 5). This should be used to calculate initial speed, by dividing it over the time tbetween the two gates, obtained from the smart timer.

Figure 5 – Measuring the distance between the two gates

1. Pull the trigger to launch the ball (figure 6) and make sure that you give people around you heads up before you do so.

Figure 6 –

#### Pull the trigger to launch

1. Note where the ball lands approximately and fix a blank paper sheet there, and put a carbon paper on top of it.
2. Launch the ball again, this time when the ball land on the carbon paper setup (figure 7) it will leave a mark.

Figure 7 – Ball Land on the carbon paper

1. Measure the distance from below the launcher to where the ball landed using the measure tape (figure 8) this is the range.
2. Place Time-of-Flight accessory where the ball lands and connect it to the smart timer as gate 2. Launch the ball again and make sure that the ball lands on the white rectangle to get the time of flight .

Figure 8 –

#### Measuring projectile range

1. Analysis/Report
2. Indicate the measured distances in meter:

Distance between the 2 photogates: = _______________ (m) (figure 5)

Height from table to launcher h = ________________ (m) (figure 9)

h

Figure 9

1. Use DATA TABLE 2 on Moodle to record the results and complete the table below (25 %)
 speed Range Time of flight (s) Speed 1 Speed 2 Speed 1 Speed 2
1. How does increasing the angle of the launcher for a given speed change the range ? (5 %)

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1. How does increasing the speed of the launcher for a given angle change the time of flight ? (5%)

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1. For the values and speed 1, calculate the theoretical expected values of and using the formulae (11) and (9) in the lab manual. (10%)

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1. Compare the expected values (theoretical) and the observed values (experimental). Give one reason to explain the eventual discrepancy (5%)

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Bonus question (10%): Give an example of projectile motion from everyday life, with theoretical explanation.

Graph 1 : height h(m) versus time t(s)

h(m) t(ms) 0 5 10 15 20 25 30 40 50 60 70 t(s) 0 5 10 15 20 25 30 40 50 60 70 h/t(m/s) 0 5 10 15 20 25 30 40 50 60 70 t2(s2) 0 5 10 15 20 25 30 40 50 60 70 h/t2(m/s2) 0 5 10 15 20 25 30 40 50 60 70

time t(s)

Height h(m)

Graph 2 : height h(m) versus time t2(s2)

h(m) t(ms) 0 5 10 15 20 25 30 40 50 60 70 t(s) 0 5 10 15 20 25 30 40 50 60 70 h/t(m/s) 0 5 10 15 20 25 30 40 50 60 70 t2(s2) 0 5 10 15 20 25 30 40 50 60 70 h/t2(m/s2) 0 5 10 15 20 25 30 40 50 60 70

t2(s2)

Height h(m)

Graph 3 : Velocity V(m/s) versus time t (s)

y(cm) 0 0.05 0.1 0.15000000000000002 0.2 0.25 0.3 0.35 0.39999999999999997 0.44999999999999996 0.49999999999999994 y(m) 0 0.05 0.1 0.15000000000000002 0.2 0.25 0.3 0.35 0.39999999999999997 0.44999999999999996 0.49999999999999994 v(m/s) 0 0.05 0.1 0.15000000000000002 0.2 0.25 0.3 0.35 0.39999999999999997 0.44999999999999996 0.49999999999999994 #REF! 0 0.05 0.1 0.15000000000000002 0.2 0.25 0.3 0.35 0.39999999999999997 0.44999999999999996 0.49999999999999994 1 #REF! 0 0.05 0.1 0.15000000000000002 0.2 0.25 0.3 0.35 0.39999999999999997 0.44999999999999996 0.49999999999999994 1 #REF! 0 0.05 0.1 0.15000000000000002 0.2 0.25 0.3 0.35 0.39999999999999997 0.44999999999999996 0.49999999999999994 1

t(s)

Velocity V(m/s)

FREE FALL and MOTION SUBJECT TO GRAVITATIONAL FORCE

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Last Updated on July 26, 2020 by Essay Pro