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- Angular Impulse and Momentum Principles To apply the principle of angular impulse and momentum to describe a particle's motion. The moment of a force about a point O, fixed in an inertial coordinate system, MO, and the angular momentum about the same point, HO, are related as follows: ∑MO=H˙O where H˙O is the time derivative of the angular momentum, HO=r×mv. Integrating this equation with respect to time yields the following equation: ∑∫t2t1MO dt=(HO)2−(HO)1 This equation is the principle of angular impulse and momentum, and it is often rearranged to its more familiar form (HO)1+∑∫t2t1MO dt=(HO)2 A centrifugal governor consists of a central rotating shaft that has two thin, pin-connected rods attached to it; a heavy sphere caps the end of each rod. (Figure 1) A centrifugal governor mechanically limits an engine's speed. A part of the engine turns the centrifugal governor, and if the speed exceeds a set amount, the height of the spheres decreases the driving force of the engine by…Somewhere DEEP BELOW THE EARTH's surface, at an UNKNOWN displacement from the Earth's center, a particle of mass m is dangled from a long string, length L; the particle oscillates along a small arc according to the differential equation d^2x/dt^2=-(pi^2/36)x. Here x refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m=3kg. The length of the string is given by L=5 meters. Whenever the particle arrives at a location of x=(pi/12) radians from the vertical, the particle has no instantaneous speed. On both sides of the vertical, that is, x=(pi/12) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion. 1. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during oscillation, making sure to label variables and constants described above. 2. Approximating to three significant digits if necessary, what is the angular frequency of this oscillator on a string? 3. Approximating…The speed of sound traveling through the sea is a function of temperature, salinity, and pressure. It is modeled by the function C = 1449.2 + 4.67T -0.055T² +0.00029T³ + (1.34-0.01T) (S-35) + 0.016D where C is the speed of sound (in meters per second), T is the temperature (in degrees Celsius), S is the salinity (the concentration of salts in parts per thousand, which means grams of dissolved solids per 1000 grams of water), and D is the depth below the sea surface, in meters. Calculate the following (Check attached image d3) when T = 10 °C, S = 35 parts per thousand, and D = 100 m. Explain the physical meaning of these derivatives.
- Use of Infinite Sequences and Series in Problem Solving of Special Theory of Relativity. A spacecraft travels fast the earth has a greater velocity (ⱱ) which approximates the speed of light. The time (to) measured in the spacecraft is different from the time (t) measured on earth. The time difference is given, to = t √1- ⱱ 2/c2 = t (1 – ⱱ 2/c2)1/2.Pendulum A pendulum swings back and forth. The angular displacement u of the pen-dulum from its rest position after t seconds is given by the function u 5 20 cos (3pt), where u is measured in degrees (Figure 14).a. Sketch the graph of this function for 0 <= t <= 6.b. What is the maximum angular displacement?c. How long does it take for the pendulum to complete one oscillation?A flywheel rotating at 500 rpm decelerates uniformly at a 3 rad/sec². How many seconds will it take for the flywheel to stop?* a. 49.36 s b. 49.35 s c. 49.37 s d. 49.40 s
- spring attached 2.00 kg block is stretched 20.0cm and released from rest on a frictionless surface. The measured period is 1.00 sec. a) What is the spring constant k? b)A student doubled the stretched length. what is the period of the spring? c) You want to make a simple pendulum and a physical pendulum which is a uniform bar, and you want same period with the spring’s period, 1.00sec. Determine the length of simple pendulum (Ls) and physical pendulum (Lp). And find the ratio of their length (Lp/Ls). d) If you doubled the length of the simple pendulum and physical pendulum, what is the period of each pendulum? e)You take these three harmonic oscillatorsto the space station and measure the period. Describe what the measured value of the period of each oscillator would be.Why?The horizontal force due to water acting on the bolt (Fh): Fh=ρ×A1×V1×V1--V2 Fh=1000×π4×0.0752×1.254×1.254+11.286( Fh)=69.472 This is the only part I did not understand how to get. Can you please explain more? I arrived with this equation, -P1A1 - P2A2 (cancelled since atmos. Pres.) +Fh = rho A1v1 (v2-v1) Why did P1A1 disappear in your solution? How did you come up with (v1 - - v2) ? What is the control volume? Why did you not do a summation of forces is equal to change in momentum but instead go immediately to getting the horizontal force acting on the bolt?A weight is attached to a spring suspended from a beam. At time t = 0, it is pulled down to a point 8 cm above the ground and released. After that, it bounces up and down between its minimum height of 8 cm and a maximum height of 24 cm, and its height h(t) is a sinusoidal function of time t. It first reaches a maximum height 1.4 seconds after starting. (a) Follow the procedure outlined in this section to sketch a rough graph of h(t). Draw at least two complete cycles of the oscillation, indicating where the maxima and minima occur. (b) What are the mean, amplitude, phase shift and period for this function? (Use a phase shift with an absolute value less than the period.) mean 16 amplitude 8 phase shift ___ period 2.8 (c) Give four different possible values for the phase shift. (Enter your answers as a comma-separated list.) _______ (d) Write down a formula for the function h(t) in standard sinusoidal form; i.e. as in the…
- Pierce (1948) mechanically measured the frequency (the number of wing vibrations per second) of chirps (or pulses of sound) made by a striped ground cricket, at various ground temperatures. Since crickets are ectotherms (cold-blooded), the rate of their philosophical processes and their overall metabolism are influenced by temperature. Consequently, there is a reason to believe that temperature would have a profound affect on aspects of their behavior, such as chirp frequency. In general, it was found that crickets did not sing at temperatures colder than 60°F or warmer than 100°F. In the following data let X= chirps/sec for the striped ground cricket and Y= temperature in degrees of Fahrenheit. X 19 19.8 18.4 17.1 15.5 14.7 17.1 15.4 16.2 15 17.2 16 17 14.4 Y 71.6 93.3 84.3 80.6 75.2 69.7 82 69.4 83.3 79.6 82.6 80.6 83.5 76.3 a. use two decimal places: Y bar =? b. use two decimal…I have data accrued from a fan could you explain to me the concepts and show me how to calculate the horsepower and work done by the fan that data was composed of below in this table? Time (s) Run #1 Velocity, Blue (m/s) Run #1 0.05 0 0.1 0 0.15 0 0.2 0 0.25 0 0.3 0 0.35 4.04E-04 0.4 4.04E-04 0.45 0 0.5 -4.04E-04 0.55 -4.04E-04 0.6 0 0.65 0 0.7 4.04E-04 0.75 8.08E-04 0.8 4.04E-04 0.85 -4.04E-04 0.9 -8.08E-04 0.95 0 1 8.08E-04 1.05 4.04E-04 1.1 0 1.15 -4.04E-04 1.2 0 1.25 4.04E-04 1.3 0 1.35 0 1.4 -4.04E-04 1.45 0 1.5 4.04E-04 1.55 0 1.6 0 1.65 -4.04E-04 1.7 0 1.75 4.04E-04 1.8 0 1.85 0 1.9 -4.04E-04 1.95 0 2 4.04E-04 2.05 4.04E-04 2.1 4.04E-04 2.15 0 2.2 0 2.25 0 2.3 0 2.35 0 2.4 0 2.45 0 2.5 4.04E-04 2.55 8.08E-04 2.6 8.08E-04 2.65 8.08E-04 2.7 8.08E-04 2.75 8.08E-04 2.8 4.04E-04 2.85 0 2.9 0 2.95 0 3 0 3.05 0 3.1 0 3.15 0 3.2 0 3.25 0 3.3 0 3.35 0…Example 9.15 A rope, to which a weight is attached, passes around a pulley 50 cm in diameter. The angular acceleration of the pulley is 18 rad/s2. If the pulley is initially rest, find a- The time required for the weight to attain a velocity of 15 m/s b- The number of revolution through which the pulley rotates during that period, c- The total acceleration of a point on the rim of the pulley 0.5 second after it was at rest.