Ib Physics, Inclined Plane

Sagar Sood IB Physics Yr. 1 IB Lab Report Due: 5th Jan, 09

Introduction / Purpose

An object tends to be in motion when there is a change in its location due to its movement. This change occurs because of a force applied on it. Motion is typically described in terms of velocity, acceleration, displacement, and time. An object's velocity (in other words its motion) cannot change unless it is acted upon by a force, as described by Newton's first law. In this lab, the type of motion that is dealt with is linear motion. Linear motion is the motion of an object in a straight line. All objects possess energy. Energy is the stored form of work in an object. In this case, the cart also stores energy in it when it is at rest in the form of potential energy. Potential energy is the energy stored by an object by the virtue of its position at different heights. More the height, more the potential energy. The energy possessed by an object in motion is known as kinetic energy. In this case, the cart possesses kinetic energy while moving down the plane. It is related by the velocity of an object as well as its mass. If either one of these increases, the kinetic energy also increases. The relationship between kinetic energy and potential energy is that as the potential energy decreases (the horizontal positioning of an object), the kinetic energy increases. In this investigation, the cart will be placed at different angles of the inclined plane. As the height would increase the cart will be

dropped without any applied force on it and a photogate on the plane will measure the time taken for the 0.050m±0.001m side of the car. In this lab, the angle of the inclined plane would be increased, hence being the independent/manipulated variable. The velocity of the cart will depend on the height, hence being the dependant/responding variable. A number of factors like the applied force on the cart (0 N), mass of the cart, friction on the inclined plane, distance of the ramp and distance at which the photogate will be placed will be kept constant, hence being the controlled variables. These controlled variables, if changed, can directly affect the motion of the cart, hence changing the velocity. The main purpose of this experiment is to find the one factor that affects the motion of the cart on the inclined plane.

In this lab,

the angle of the inclined plane will be the one factor that will be changed, hence affecting the motion of the cart.

Hypothesis As the angle of the inclined plane will be increased, the height would also increase. This would increase the velocity of the cart moving down the plane. This would happen because as the height would increase the potential energy of the cart would also increase. As the potential energy would increase, the cart would have more energy stored in it which would be converted in the form of kinetic energy. As kinetic energy is related by the mass and the velocity of an object, the time taken for the cart’s motion would decrease, hence increasing the velocity of the cart (mass of the cart is kept constant).

Design

Materials Required  Photogate(±0.0001s)  Meter stick (±0.001m)  Cart

 Inclined Plane(1m±0.01m)  Stand

 Protractor(±1°)

Procedure 1. When all the materials are acquired, set up the apparatus as the figure below. Measure

2.

the angle of

the inclined plane with the help of the protractor.

(In

our case, the first angle is 12°±1°)

3. Measure the length of the side of the car.(in our case it was 0.050±0.001m) 4. Set the photogate at almost 2/3 rd the way down the ramp and note the point at which it is set.(in our case, it was set at 0.50m±0.01m)

5. Put the car at the top of the inclined plane and set the photogate at zero. 6. Without any applied force, release the cart and let it move all the way down the ramp. 7. Record the time in the timer of the photogate and set the photogate to zero again. 8. Without changing the position of the photogate on the ramp, repeat the steps 4, 5 and 6 two more times in order to get 3 trials. 9. After measuring 3 trials for the first data point move on to the next by changing the angle of the ramp(fix the ramp in the next possible hole of the stand, in our case the next data point was 17°±1°) 10. In total measure down 6 data points with 3 trials each.

Data collection

The table below shows the time taken for the 0.05cm side of the car to pass through the photogate at different angles of the inclined plane.

Time elapsed(s)

Angle of the

Trail 1

Trial 2

Trial 3

Average

Uncertaint

time(s)

y

ramp(°)

(± s)

12

0. 0405

0. 0407

0.040 8

0. 0407

0.002

17

0.0 331

0. 0334

0.0 331

0.0 332

0.002

22

0. 0285

0. 0287

0.02 84

0.02 85

0.002

30

0. 0244

0.0242

0.0243

0.0243

0.001

36

0.0225

0. 0222

0. 0222

0. 0222

0.002

42

0.02 07

0.02 06

0.02 07

0.02 07 

0.001

± 1° Angle of

± 0.0001 Average

Velocity

Uncertainty

-1

-1

(ms )

(±ms )

±0.002

Instantaneous

Uncertainty

Velocity

(±ms )

-1

the ramp

time

( °)

(s)

12

0.0407

1.2

0.03

2.5

0.1

17

0.0332

1.5

0.04

3.0

0.1

22

0.0285

1.7

0.04

3.5

0.2

30

0.0243

2.0

0.05

4.1

0.2

36

0.0222

2.3

0.05

4.5

0.2

42

0.0207

0.06

±0.0002

4.8 

0.3

± 1°

2.4 

-1

(ms )

0.05

0.2

With help of the average time, the velocity of the cart is found and shown below in the table.

Data processing  In all cases Data Point 1(12 °±1 °) has been taken into account Average Time=

Sum of trials / Number of trials =

(0.0405+0.0407+0.0408) / 3

=

0.0406666667

=

0.0407s

Uncertainty of average = (Largest number. – Smallest number) / 2 = (0.0408 – 0.0405) / 2 = 0.00015 = ±0.0002 = 0.0407s ± 0.0002s As shown in the data table, the uncertainty is taken to be 0.002s. This is calculated my taking out the average of all the trials and data points. (0.002 + 0.002 + 0.002 + 0.001 + 0.002 + 0.001) / 6 =

0.002s

Velocity = Distance / Time = (Side of car) / (Time) = (0.050m) / (0.0407s) = 1.2 ms

-1

Instantaneous Velocity = [(Distance of the car side / Time elapsed) / Distance of the position of the photogate]

= (0.050m / 0.0407s) / (0.50m) OR = (0.050m / 0.0407s) X 2

(Velocity X 2 = Inst. velocity) = 2.457002487 = 2.5 ms

-1

Uncertainty = [(±0.001m) (±0.0002s)] / (±0.01) => [(±0.001m) (±0.0002s)] = (Uncertainty #1) +

(Uncertainty #2)

(Value 1) =

(0.001)

X 100

(Value 2) +

(0.0002)

X 100 (0.050m)

(0.0407s)

= 2.49 % = 2.49 % of 1.23ms

-1

= 0.030601 -1

= ±0.03 ms …………………………………………. (Uncertainty for velocity) -1

Uncertainty for Inst. Velocity = (± 0.03 ms ) / (±0.01)

= X 100

(0.03)

+

(0.01)

-1

(1.23 ms ) =

4.44 %

=

4.44 % of 2.5ms

=

0.1109756098

=

±0.1

=

2.5 ms

-1

± 0.1 ms

(0.50m)

-1

-1

Uncertainties of other data points = 0.1+ 0.1 + 0.2 + 0.2 + 0.2 + 0.3

6 = 0.1833333 = ±0.2………………………. (Average uncertainty) Slope of the Graph = Rise / Run = (36.5 – 12) / (4.8 – 2.5) = (24.5 / 2.3) = 10.7 ms

-2

(Value of acceleration due to

-2

gravity = 9.8 ms ) Percent Error = [{Theoretical Value – Calculated Value} / Theoretical Value] x 100 = [(9.8 – 10.7) / 9.8] x 100 = 9.2 % Error

CONCLUSION

Overall the experiment was carried out with minimum errors. There were six data points with three trials each. The investigation was carried out as stated in the procedure. The experiment was related to find one factor that affects the motion of a cart on an inclined plane. The factor used in my experiment was the increase in angle of the inclined plane (or the height of the ramp). The data and the graph clearly show that as the angle/height of the ramp increases the velocity of the cart increases as well. This means that they are directly proportional. In my experiment the angle of the ramp was increased which increased the height of the ramp. As the height increased the potential energy of the cart increased as the main factor in potential energy is the height. This energy was further transformed into kinetic energy or the energy of motion. In other words as the height increased, the potential energy increased which furthermore increased the kinetic energy. As kinetic energy is directly linked to the velocity of an object, it is safe to say that as the kinetic energy increased, the velocity of the cart increased. This proves my hypothesis correct.

Evaluation As it can be seen from the graph and the data table that there were some errors in the investigation. The percent error that was calculated to be 9.18 % assures the fact that there were flaws in my experiment. One big error was that the whole ramp setup was never flat and straight. Because of this, the car was at different heights hence having different potential energy and furthermore changing the velocity of the cart. Also, it was almost never that the cart left the top of the ramp without an applied force. This changed the velocity of the cart hence altering the values in the data table. Also, during the

experiment a couple of times, the cart slammed into the photogate. This changed the position of the photogate by a centimeter or two. This hence gave different values of the time which later changed the values of the calculated instantaneous velocity.

Self-improvement The above errors can be improved by a number of precautions. Before starting the experiment the ramp should be completely flat and straight, a ruler should be used to align if necessary. Even during the experiment, it should be made sure that the ramp is aligned as after each trial the high speed of the cart changes the alignment. Also it should be made sure that the cart leaves the top of the ramp without any applied force. The hand should be perfectly still before leaving the cart so that the cart does not experience exerted force. The position of the photogate should always be noted down and even if the cart slams into the photogate, it should be positioned back to the same point and the trial should be re-done.