PHYSICS IA – Nish Dedhia 11A

Personal Engagement –

Cycling is the use of a bicycle for transport, recreation, or sport. Cycling can be
enjoyed by almost everyone, regardless of their age or your physical ability. Cycling
is a very effective form of exercise. Cycling has always been one of my favourite
hobbies since childhood because it is known to reduce stress and help you stay
active. I have always wondered about the thrill and excitement I experience when I
travel downhill as compared to travelling on a flat surface. The relationship between
the steepness of the hill and the final speed while travelling downhill has always
evoked a sense of curiosity in my mind.
Research Question –
How the final speed of an object/ball varies with the height of an inclined plane?
Hypothesis –
The greater the height of the inclined plane, the higher the final speed of the object.
It is also hypothesised that as the angle of the inclined plane increases, the speed of
the object will also increase which results in shorter time for the car to travel down
the ramp.
Theory –

Potential energy is stored energy and the energy of position — gravitational energy.
Gravitational Energy is energy stored in an object's height. The higher and heavier
the object, the more gravitational energy is stored. Kinetic Energy is energy stored in
the movement of objects. The faster they travel, the more energy is stored.
VARIABLES

Dependent Variables –
Final speed at which the object hits the ground. The final speed of the object will be
found using the equation ->

Independent Variables –
The angle of inclination of the plane

Constants –
Object - block
Ramp (Surface)
Distance of the Ramp – (Start & End Point same)
Air Speed
MATERIALS –

1. Stand – To hold the ramp and to increase/decrease its height

2. Inclined Plane/Ramp - For the object to slide down (Eg. Ruler)
3. Stop watch - to time the object (start - finish)
4. Measurements tape - to measure out the fixed distance the object will travel
over the ramp
5. Protractor – to measure the angle between the inclined plane and the surface
6. Marker - To mark the start point and end line or point

Fig. 1
PROCEDURE

1. Setting the apparatus as shown in Fig. 1

2. Calculate the angle of inclination using the protractor between the surface and
ruler and record it in the table

3. Place the object at the start point on the inclined plane

4. Release the object with no extra force and simultaneously start the stop watch

5. Press the stop button when the object reaches the end point or when the front
of the object touches the surface

6. Record the time taken for the object to reach the end point

7. Construct a table with the values of the time taken, next to the relevant height.

8. Repeat from step 2, 2 times to obtain 3 results for the same height.

9. Calculate the Average Time in the table.

10. Calculate the Final Speed using the equation ->

 11. Re-adjust the inclined plane with a greater height and repeat the same steps

Table –

Height of the Angle of Trial 1 (s) Trial 2 (s) Trial 3 (s) Avg. Time Final S
Ramp (m) Inclined (s) (m/s)
Plane
(degrees)

The experiment will be conducted under lab conditions and along with lab
equipment. Therefore, the uncertainties have been determined on the basis of lab
equipment available.

The first assumption we make is that the frictional force between the inclined plane
and block would be almost negligible since both the surfaces are extremely smooth,
therefore implying how no work Is done by the frictional force.

Frictionless block –

The block can only accelerate in the direction along the plane. The net force in the
forward direction will be mass*acceleration and the net forces in the y-direction will
be zero since the Normal Force = Vertical component of the weight and hence the
block is at rest. The only force acting towards the x direction is a component of the
gravitational force. This means that the forces in the x-direction will be:
Gravity gives potential energy to the object whereas kinetic energy of an object
depends only upon its mass and its speed. The formula for potential energy due to
gravity is PE=mgh and KE =1/2*m*v*v. Therefore, the higher an object goes the
more gravitational potential energy it gains. When it falls, its potential energy is
converted into kinetic energy and since the law of conservation of energy states that
energy can neither be created or destroyed, it can only be converted. Therefore, the
object will move at a faster speed since the difference in potential energy is equal to
the difference in kinetic energy.
Therefore, the equation for the final speed of the object is ->

The value of u=0 since the object is initially at rest and hence the
initial velocity=0
FRICTION BLOCK

The frictional force is the force that prevents the disk from slipping. However, not all
the potential energy is converted into kinetic energy in this case, as some of this
energy is lost as heat from the friction between the ramp and the object as the object
goes down the ramp and sound as it travels through the inclined plane.
In this scenario we will consider that the object slides without slipping, hence the
frictional force will be a static friction force.

Here μs is the coefficient of static friction.

When the angle of inclination of the ramp is small, the force of friction between the
object and the ramp has greater potential to prevent the object from moving. When
an object rests on a surface like the ramp, the ramp exerts a perpendicular force
from the ramp called ‘normal force’ on the object, this force is greater when the angle
of inclination is smaller. This happens due to the force of gravity on the object that is
be split between horizontal and vertical components. Therefore, when the ramp is
steep, the force of gravity can more easily overcome the force of friction and hence
gravity will cause the object on an incline to move down the slope faster than a flat
slope.
The steeper the ramp the larger the amount of the sliding force. When the ramp is
vertical the sliding component and equals the weight force.
The greater the height of the inclined plane, the higher the final speed of the object.
This is because gravity is pulling the object straight down and friction is preventing
the object from slipping down. The net force (the sum of the weight and normal
force) acting on the object is large enough to make the car to accelerate down the
ramp.

The value of the Normal Force can help us to calculate the Maximum value of the
frictional force since it cannot be larger than the component of the gravitational force
in the direction of the inclined plane. The static frictional force is called a constraint
force. This force will exert such a value which will cause the block to slide down
continuously without any slipping, upto a maximum value. Here is the equation for
the net forces in the x-direction ->

This equation can then be used to find the acceleration when you substitute the
value of the frictional force.
UNCERTAINTIES / ERRORS

Errors could occur due to the reaction time, wherein time could be calculated
incorrectly since the time could be wasted when the stopwatch is started and
stopped

There is a possibility of random errors in the time measurement due to the difficulty
in starting and stopping the clock operated by hand.

The measurement uncertainty involved in the Stopwatch is (+/- 0.01 seconds

The measurement uncertainty involved in the one metre ruler is (+/- 0.5 cm)

Precautions / How to Avoid Errors –

Repeated Readings can eliminate the random errors such as reading errors that may
occur while performing the experiment. Moreover, the correct way of reading the
protractor and meter rule perpendicularly can ensure more accurate results since it
overcomes the parallax error. The instability of the object can be overcome by
adjusting the ruler firmly to the stand and fixing its position at the surface as well.
Also, the ruler needs to be placed straight and parallel to the surface with no slant
placement. Moreover, you need to ensure there is no extra force applied while
releasing.

Conclusion –
An increase in height of an object from a surface in the presence of a gravitational
field corresponds to an increase in the potential energy of the object. When the
object is left to slide down the higher, more inclined ramp to the surface, this higher
potential energy can be converted into correspondingly higher kinetic energy.

Since kinetic energy is calculated from the mass of an object and its speed, the
higher the ramp, the faster the final speed of the object down the ramp will be.

Bibliography –

https://www.wired.com/2014/07/a-rolling-object-accelerating-down-an-incline/

https://www.quora.com/Does-dropping-a-ball-from-a-greater-height-increase-its-
speed

https://www.ukessays.com/essays/physics/effect-height-velocity-experiment-
7587.php#_Toc396914186

https://van.physics.illinois.edu/qa/listing.php?id=183

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https://www.scientificamerican.com/article/speedy-science-how-does-acceleration-affect-
distance/

http://www.academia.edu/28424874/Kinematic_Experiment_Lab_Report_How_can_the_hei
ght_of_a_ramp_affect_the_accleration_of_a_table_tennis_ball