Physics assignment
m21q8
PHYS218_Fall2020_Assessment3.docx
Semester: Online Fall 2020
Course Code: PHYS218
Course Title: Modern Mechanics
Experiment #: Assessment 3
Experiment Title: INCLINED PLANES and
CONSERVATION OF ENERGY
Date: ………………………..
Name: ……………………….
ID #: ………………………
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Report Grade: …….. /100 |
PART A (50%)
1. Introduction
If a body needs to be propelled up an inclined plane, it is not the body’s full weight W which needs to be overcome, but only the component which acts parallel to the plane F1. The fact that this component is less than the weight is more pronounced the smaller the inclination α of the plane becomes. In this experiment students will determine this force, by measuring the maximum and minimum masses for different angles.
2. Objectives
· Determine the component F1 of the weight of an object which acts down an inclined plane as a function of the angle of inclination α.
· Plot the ratio of the component F1 to the weight W as a function of sin α.
· Compare experimental and theoretical value of weight W
3. Experimental setup:
· Inclined Plane Apparatus.
· Precision Dynamometer 5 N.
· Set of Weights 1 g to 500 g
4. Theory
Figure 1 – Experimental setup
The vector differential between the weight and the component down the plane is represented by the component normal to the plane F2 , see Fig. 2
Figure 2. Resolution of the weight W into vector components parallel to the plane, F1 , and normal to the plane, F2
The magnitudes of the forces are given by the following relationships:
(1)
(2)
In this experiment, the body is suspended from a cord which runs over a pulley. The force along the plane is then compensated for by weights on a weight holder suspended from the other end of the cord. Since the friction between the body and the inclined plane is of importance, the value used for the measurements is an average of the lowest and highest values, where the component of the force down the plane is just enough to stop the body sliding down the slope and when it is just enough not to drag it up the slope.
To determine force F1 from measurement can be used following equation:
(3)
where WP is weight of pan in Newtons, mavg is average mass in kilograms, and g is free – fall acceleration
5. Experimental Procedure
a) Hold the dynamometer vertical and calibrate the zero point.
b) First determine the weight in Newtons W of the roller and then the weight of the pan WP .
c) Set the inclined plane to an angle of inclination α=10°.
d) Put the roller on the inclined plane, run the cord over the pulley and place enough weights in the pan at the other end of the cord so that the roller cannot roll either up or down the plane
e) By removing or adding weights to the pan, find out the minimum and maximum mass of the weights at which the roller is just prevented from rolling up or down the plane. Enter the values for the maximum and minimum masses into table 1 given at the report.
f) Keep steeping the angle of the plane in steps of 10° (The maximum angle that can be set is 44°). Find out the maximum and minimum masses which keep the roller still for each angle and enter the values in table below (Table 1).
7. Analysis/Report
a) Make a note of these values using DATA Table 1 on Moodle.
Weight of roller W in Newton = _______ ______________ (2%)
Weight of pan WP in Newton = _________ ____________ (2%)
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α (°) |
mmin(g) |
mmax(g) |
mavg(g) |
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10° |
11 |
20 |
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15° |
30 |
45 |
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20° |
60 |
75 |
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25° |
80 |
100 |
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30° |
99 |
125 |
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35° |
122 |
150 |
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40° |
140 |
170 |
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44° |
154 |
192 |
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b) Use DATA Table 1 on Moodle to record the results and complete the table below, find the average value mavg and record it in the table below. (8 %)
Table 1
c) Determine the force along the plane F1 from measurement using formula (3) and plot the graph F1(N) versus sin(α) below using the indicated scale (8%) Table + (8%) Graph
d) Use the slope found on graph and the equation (1) in the manual to find out the weight W of the roller from the graph. (10%)
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e) Compare the weight of the roller directly measured by the dynamometer and the value obtained from the graph. Which one is more reliable? Explain (12%)
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PART B (30%)
1. Introduction
Energy (𝐸) is a scalar physical quantity. It is a property of objects and has various different forms. The form of the energy can be Mechanical, Heat, Chemical, Magnetic, Electrical, Atomic, Nuclear, or something else. The most important property of Energy is being conserved. This means, the energy can’t be created or destroyed. It can “ONLY” be transformed (or converted) from one form to another. For example: Mechanical energy can be converted to Electrical, like the electric generator on your bicycle. Vice versa, energy can be converted from Electrical to mechanical, like ventilators. As a result to the conservation of energy, the total energy of any system is always constant and does not change.
(1)
Therefore, to study the properties of any system, the scientists do measure, or calculate, the change of its energy. If the change of energy is not zero, this means that there is an “external” work (𝑾) done on the system from the surroundings, leading to kinetic energy (𝑲). Inside the system, there is always an “internal” work, due to the interaction forces between the particles inside the system, leading to potential energy (𝑼). In fact, this makes the source of the energy to be the forces. If there are no forces, from outside or inside the system, the system will have no energy.
In nature, every system has an energy, because the forces are always there, and they keep acting on any system and doing a work on it. In this experiment students will prove that the total energy is not changing. They will prove conservation of energy, by measuring final speed of an object depending on its’ mass and initial height.
2. Objectives
· To verify the energy principle.
· To calculate the error when measuring the total energy.
· To conclude how increasing of mass affects total energy
· To conclude how increasing of initial height affects total energy
Experimental setup:
Figure 1. Roller Coaster track setup
· Roller Coaster Complete System (car, panel,...).
· Photo-gate Head.
· Smart timer
· Tape measure
· Spring balance
3. Theory
Mechanical Energy has two parts:
(2)
· Kinetic energy (𝑲): the energy to change the system position per time. This means it is depending on the speed of the system (𝒗). It can be calculated as
(3)
where 𝒎 the mass of the object, and 𝑣 is its speed.
· Potential energy (𝑼): the energy stored in the system, due to the interaction forces inside the system. It can be calculated as
(4)
Where 𝒈 is gravitational acceleration (𝟗.𝟖𝟏 𝒎/𝒔𝟐) and 𝒉 is the height from reference point.
If we ignore the friction and consider only gravitational force, the total energy of the system will not change (equation 1), meaning that
(5)
The kinetic can be transferred to potential, and vice versa. Then, if the kinetic energy is maximum, the potential energy must be minimum. The opposite is also true, if the potential energy is maximum, the kinetic energy must be minimum. This is explained in figure 2.
Figure 2 shows how one kinetic is changed into potential energy, or vice versa, during motion.
Figure 2. Change in energy
In the special case of an object released from rest () sliding to the bottom of a roller coaster (), the equation 5 leads to:
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· (6)
A car is started from rest on a hill (roller coaster track). Speed of the car at the bottom of the track is measured using a photogate connected to a Smart Timer. The potential energy is calculated from the measured height and the kinetic energy is calculated from the speed. The total energy is calculated for two points on the track and compared.
4. Experimental Procedure
Initial measurement
1. Measure the initial position of the car (𝐻) (Figure 3). Be careful to record the height in meters, not in inches or centimeters.
Figure 4. Measuring the height of the car at flat part
Figure 3. Measuring the height of the car at initial position
2. Measure the height of the car of a flat part, at the bottom of the track (ℎ), from the table (Figure 4)
3. Measure the car weight using spring balance. Do not forget to calibrate the instrument before using it, using the screw on top to bring the mark to zero position of the scale.
4. Change of Total Mechanical Energy as a function of the mass:
a) Place the car at the top (Figure 5) and release it from rest.
b) Use the Photo-gate and Smart Timer to measure the speed of the car on the flat part, at the bottom of the track (Figure 6).
c) Attach the given weight to the car and repeat steps 4 and 5.
Figure 6. Final position of the car
Figure 5. Initial position of the car
d) Record your results and complete table 2.
5. Change of Total Mechanical Energy as a function of the height:
a) Place the car at the top (Figure 5) and release it from rest.
b) Repeat step a) by placing the car in different height and releasing it from rest.
c) Use the Photo-gate and Smart Timer to measure the speed of the car on the flat part, at the bottom of the track (Figure 6).
d) Record your results and complete table 3.
5. Analysis/Report
1. Fill in the table below table using DATA Table 2 on Moodle. (2%)
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Mass of the car M(kg) |
0.04 |
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Height at the top H(m) |
0.489 |
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Height at the bottom h(m) |
0.078 |
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Initial height (m) | |
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Final height (m) |
0 |
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Initial velocity |
0 |
Table 1
2. Change of Total Mechanical Energy as a function of the mass:
a) Complete the table below and calculate errors (10.5%)
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M (kg) |
M + 0.05 (kg) |
M + 0.1 (kg) |
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0 |
0 |
0 |
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0 |
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0 |
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Table 2
b) How does increasing the mass of the car change the total energy? (2%)
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c) How does increasing the mass of the car change the speed of the car at the bottom? (2.5%)
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3. Change of Total Mechanical Energy as a function of the height
a) Record your results and plot the graph versus using the indicated scale. (6%(table)+2%(graph))
b) Use the slope from the graph and the equation 6 to find the Earth’s gravity constant. (5%)
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PART C – SIMULATION (20%)
Use the link below and download the .jar file and run the java simulation:
https://phet.colorado.edu/en/simulation/energy-skate-park
· Check the “Grid” option in the right side tools palette in order to measure the height of the skater.
· Drag and drop the parabolic track in order to set its minimum at 0 meter.
· Choose “Earth” as location and use the value of 9.81 N/Kg for the gravity constant.
· Set the skater mass to 50Kg using the button “Edit Skater”.
· Use the “Energy Vs. Time” button to fill the table below: (14%)
(You need to show a detailed calculation of the speed)
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Skater Height (m) |
Potential Energy (J) (Measured) |
Kinetic Energy (J) (Measured) |
Speed (m/s) (Calculated) |
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6 |
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5 |
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4 |
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3 |
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2 |
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1 |
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0 |
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1) How increasing the mass of skater will change its potential and kinetic energy? (2 %)
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2) What can you tell about total energy of the skater? (4 %)
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Bonus question (5%):
A 30 kg child, starting from rest, slides down a 4m high frictionless slide.
1. How fast is he going at the bottom? (2.5%)
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2. Now he slides down the same slide with friction, and his speed at the bottom is 5 m/s.
How much thermal energy has been produced by friction? (2.5%)
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0.17299999999999999 0.25800000000000001 0.402055
sin α
F1 (N)
hi(m)
Vf2 (m/s)2
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