1.2.1 A big 18 wheeler truck collides head-on with a small Kia Picanto car. The Kia Picanto car suffers the greatest damage while the truck does not as illustrated below Learners were asked to explain why the small Kia Picanto car suffered the greatest damage than the truck. The statements below are learners' explanations:
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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…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…
- Principle of Linear Impulse and Momentum for a System of Particles To apply the principle of linear impulse and momentum to a system of particles. Integrating the equation of motion, as applied to all particles in a system, yields ∑mi(vi)1+∑∫t2t1Fidt=∑mi(vi)2 where mi is the ith particle's mass, vi is the ith particle's velocity, and Fi is the external force that acts on the ith particle. This relationship states that the sum of the initial linear momenta, at time t1, and the impulses of all the external forces acting between times t1 and t2 is equal to the sum of the linear momenta of the system, at time t2. If the system has a mass center, G, the expression becomes m(vG)1+∑∫t2t1Fidt=m(vG)2 This expression allows the principle of linear impulse and momentum to be applied to a system of particles that is represented as a single particle. Two blocks, each of mass m = 6.90 kg , are connected by a massless rope and start sliding down a slope of incline θ = 36.0 ∘ at t=0.000 s. The…Suppose we got the following data during a test of a 2- stroke engine in which gas is usedas a fuel:Diameter of the piston = 149 mmStroke length = 179 mmClearance volume = 0.88 literrpm of the engine = 302Indicated mean effective pressure = 6.0 barGas consumption = 6.0 m3/hCalorific value of the gas (fuel) = 16990 kJ/m3Make a clear sketch the geometry of this engine using the data and determine thefollowing:i. Indicated power developed by the engine in watt.ii. Air Standard Efficiencyiii. Indicated thermal efficiency of the engine.The complete slide- back and forth motion of a single reciprocating compressor piston completes in a 2-sec period. The volume displacement of the piston though the piston cylinder is 8,902.63 in3. The stiffness of crank is said to be equal to 65.5N/m and the mass of the said piston is at 10kgs. Obtain the following 1. Plot the graph of the following relationship: A) Position vs Time graph B) Velocity vs Time C) Acceleration vs Time
- 1) Is it possible to prescribe the velocity v0, so that the pendulum keeps rotating with alpha = pi/2 Explain clearly why? Given: L, g, and m. 2) After transient motion, the pendulum settles at steady state rotation atalpha = pi/3. Find the initial velocity v0. Given: L, g, m, sin(pi/3) = (squareroot(3)/2), cos(pi/3) = (1/2). [Hint: Use the conservation of energy and the 2nd Newton’s law.]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?7. Consider the statement “An extraterrestrial astronomer surveying our solarsystem with the Doppler technique could discover the existence of Jupiter with just a fewdays observation.” Does this statement make sense? Why or why not?
- Power Engineering - ABEN 3411 Illustrate and discuss the principle of operation for diesel and gasoline engine.The dependence of the tensions t (units: N) in a structure on the external forces f (units: N) follows the linear system Ct=f, where both t and f are 5 by 1 column vectors. The coefficient matrix C has been determined to be [ 11 14 20 -5 -19 ] -5 7 -3 5 -6 4 -5 13 -2 -10 0 0 0 12 -10 0 0 0 0 14 By how many N would the external force f2 need to be decreased (while all other external forces stay the same) in order to decrease the tension t3 by 94 N?27-(a) A body of weight 440 N body moving to the left with a velocity of 10 m/s collides with another body of weight 760 N body which is at rest. After impact the body which is moving before impact comes to rest. Find the final velocity of body after impact and the coefficient of restitution . (b)A vehicle of mass 21 tonnes runs into a buffer stop having two buffer springs connected in series each of 1750 kN/cm and 2200 kN/cm stiffness respectively. Find the maximum compression of the springs, if the vehicle is travelling at 90 km/hr. Also calculate the load acting on the spring. a,Solution The final velocity of body after impact in m/s is The coefficient of restitution is b,Solution The maximum compression of the spring in mm is The load acting on the spring in kN is