In: Physics
3Objectives•To determine the relationship between kinetic, potential, and total mechanical energy for a cart on an incline.•To determine the work done by friction on a sliding cart.•To show that energy is not conserved when a non-conservative force, like friction, is acting.Procedure: Energy of a cart withoutf riction In this experiment, we will assume that friction is negligible, and that there are no non-conservative forces at work.The motion of a cart rolling down an incline will be examined using real-time velocity and position values from a motion sensor. Examining the position and velocity of the cart as it rolls down the track allows us to also determine the energy of the cart. In this experiment you will examine the transition between gravitation potential energy and kinetic energy as the cart rolls down an incline.1.Figure 1 was set up in real time, where the ramp was inclined at an angle of 8.5°, and the mass of the cart is 0.250 kg. A Motion Detector was attached to the upper end of the track.As the cart slides down the track, the motion detector ispre-programmed to measure the distance (position) of the cart from the bottom of the ramp –see (d) infigure 1.2.Gravitational potential energy depends on position, and kinetic energy depends on velocity. The cart was released,and the position and velocity of the cart were measured with the motion sensor software. Time(seconds)Position(meters)Velocity(meters/second )
0.866658 1.273902 0.265542
0.899991 1.256238 0.471058
0.933324 1.239259 0.557238
0.966657 1.219022 0.618978
0.99999 1.197756 0.667428
1.033323 1.174775 0.720021
1.066656 1.14905 0.752035
1.099989 1.124183 0.771615
1.133322 1.098115 0.802199
1.166655 1.070846 0.8365
1.199988 1.042034 0.866512
1.233321 1.013222 0.901099
1.266654 0.982867 0.959695
1.299987 0.948738 1.006286
1.33332 0.915639 1.046589
1.366653 0.878766 1.080032
1.399986 0.842923 1.094753
1.433319 0.806908 1.141773
1.466652 0.766777 1.191794
1.499985 0.728361 1.266254
1.533318 0.682056 1.33071
43.Now, it’s time to plot the PE, KE, and total ME of the cart as
it rolls down the track.To do this, let’s first convert each
position, d, to a height so we can calculate the potential energy
of the cart. Open the data above in excel and create a new column
labeled height. Using equation 7,convert every position measurement
to the vertical height of the cart. In excel, make sure you use
0.1500983 (radians) for your angle, θ,Instead of 8.5°(degrees).
4.Create another new column titled Kinetic Energy. Create a formula which grabs each velocity value and, using your measured mass, calculates the kinetic energy of the cart(equation1).
5.Next, create another new column that calculates Gravitational Potential Energy as the cart rolls down the incline. Create a formula which multiplies the height by the mass of the cart and gravitational acceleration(equation 2).
6.Finally, create a third new column titled Mechanical Energy, which is just be the sum of your two columns, Kinetic Energy and Gravitational Kinetic Energy.
7.Create a line graph of kinetic energy versus time, potential energy versus time,and mechanical energy vs time on the same graph. Under your graph options, be sure to show a legend, so whoever reads your report will have no trouble determining which line is which.Attach the graph with your lab submission.
8.What is the approximately slope of your kinetic energy graph? What does this suggest about your cart’s kinetic energy as a function of time?
9.What is the approximately slope of your potential energy
graph? What does this suggest about your cart’s kinetic energy as a
function of time?
10.Analyze your graph carefully. What is the approximate slope of
your mechanical energy graph? What does this suggest about your
cart’s total mechanical energy?
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Refer to the illustration below. Light enters the stacked transparent plates at an angle of from the normal at location zero cm in the x direction.
In: Physics
for materials class
Manipulating strength
a. Using words and visuals, briefly describe 4 strategies to increase the strength of a metal.
b. What do these strategies have in common in terms of their mechanism?
c. Use a plot to discuss the trade-off between strength and ductility in metals. Explain why this trade off occurs based on the mechanism of plastic deformation in metals.
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5 rems per year whole body occupational dose is the generally agreed limit by the standard setting bodies. State your opinions on this limit; do you agree with it?
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A small meteorite (30 kg) is falling through the earth’s atmosphere. It is moving very fast - in fact, faster than the terminal velocity it would have reached if had been dropped from a great height. In a situation like this, the drag force is stronger than the weight. At one moment, the magnitude of the meteorite’s acceleration is 4.0 m/s2. You need to calculate the magnitude of the drag force on the meteorite.
consistent with the coordinate system in the free-body diagram. (That is, add in all the forces in the positive direction and subtract all the forces in the negative direction.)
magnitude of the drag force. Type out the equation with all known numbers inserted in their proper places and then just state the answer.
.
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A cannonball is fired at a cliff 1000 m away and strikes it 250 m above the level ground 5 seconds later.
a. What is the angle (in degrees) with which the cannonball was fired, with respect to the level ground? (g = 10 m/s2)
b. What was the approximate initial speed (in m/s) with which the cannonball was fired? (g = 10 m/s2)
c. Which time (in seconds) below is the closest to the time after firing that the cannonball reaches (or would reach) maximum height? (g = 10 m/s2)
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Big Ben in London is the most accurate mechanical clock of its size. The 300-kg hour hand is 2.7 m long, and the 100-kg minute hand is 4.2 m long. Treat each hand as if it were a thin rod. Calculate the rotational kinetic energy of the two-hand system.
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Derive the Jones matrix of a liquid crystal cell?
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Why can gravitational potential energy be ignored in a verticle spring with a hanging mass? My TA mentioned something about no work being done by GPE, but that doesn't really make sense. Also, the assignment is asking for it to be explained conceptually, not with equations. Thanks!
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A 65.0 kg man is riding on a 12.5 kg bicycle. Together they have a kinetic energy of 2.80 x 10^3. If the bicycle has wheels with radii of 0.450 m, then their frequency of rotation is
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Calculation of half-life for alpha emission using
time-independent
Schrodinger Equation using the following following
information:
Radionuclide: 241-Am (Z=95); Ea = 5.49 MeV; Measured
Half-Life~432y
Follow the steps involved and show your work for each subset
question, not the
final answer:
(a) Evaluate the well radius [=separation distance (r) between the
center of
the alpha particle as it abuts the recoil nucleus];
(b) Evaluate the coulomb barrier potential energy (U) for the
well;
(c) Estimate the separation distance (r*) from the center of the
potential well
where the coulomb potential equals the energy of the alpha
particle;
(d) Assuming a square shaped single barrier of height “U”, evaluate
the
tunneling probability by solving for the transmission coefficient
and use of
the associated separation (=r*-r);
(e) Calculate the frequency with which the alpha particle strikes
the well
boundary to try to get out of the well;
(f) Calculate the half-life and compare it with the known half-life
for alpha
emission from 238U;
(g) Use the spatially-averaged effective approximation for the
height of the
barrier by integrating the variation of “U” with distance from “r”
to “r*” and
re-calculate the half-life and compare it with the known half-life
for alpha
emission from 238U;
(h) Approximate the hyperbolic shaped barrier variation outside of
the well
by breaking them up into 5 progressively reduced height square
shaped
barriers, each with a width = (r*-r)/5 and calculate the
tunneling
probabilities associated with each segment;
(i) Re-calculate for the half-life combining the probabilities from
each of the 5
bins, and compare the value with the known half-life.
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What must be the position of an object in order that it may be seen distinctly through a +9.0 D lens placed 2.9 cm in front of an eye, the eye being accommodated for a distance of 35.5 cm? Give your answer in cm as a distance to the lens.
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Marc drives like a maniac. His defense is always "It’s OK, I know the physics of driving so I do it safely". Marc is coming up to a horizontal turn of radius r = 150 m. Since Marc is a physicist, he just knows the coefficient of static friction between the tires and the road is µ = 0.45. If the center of mass of Marc’s car is xcm = 60 cm above the ground and his car’s wheel base is ` = 1.3 m, determine the following:
(a) a formula for the maximum speed Marc can complete the turn without flipping the car.
(b) a formula for the maximum speed Marc can complete the turn while remaining on the road (hint, you will have to compare the value from two formulas).
(c) whether Marc can safely complete the turn if his speed is 100 km/h? What about at 80 km/h?
(d) Show that if µs < ` 2xcm , then it is impossible to flip your vehicle.
(e) The above ratio is something that vehicle engineers must be aware of (as it is a safety thing). Moving vans, obviously, have a much higher center of gravity, however, due to width constraints (width of lanes on the road, parking spots, etc), they are not able to make the wheelbase that much wider. If the wheelbase of a moving van is 2 m and it’s center of mass (when modestly loaded) is 5 ft, is it able to flip (using the same µs as above)?
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The weight of an astronaut on Earth surface is 950 N. What is the astronaut weight in a satellite orbiting Earth at an altitude of 500km with a speed of 450 m/s? (g=9.8 m/s2 and REarth = 6400 km). Select one: a. 790 N b. 815 N c. 852 N d. 1020 N
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