2- find the center of mass, the velocity of the center of mass, the momentum the kinetic energy of the following system: m₁ = 1 kg T₁=1+2j+3 k v₁ = 2î+3ĵ m₂ = 1 kg T₂ = 1-j+ k Sudjas v₂ = 2) + 3k
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- This most likely is made to be a probelm about mx''+bx'+kx=f(t) m = mass b = friction k = spring constant 4. A mass weighing four pounds stretches a spring 24 in. Suppose the mass is atequilibrium and is set into motion with a velocity of 6 inches per second. The mass is in a mediumwhere friction is small, and we assume it is zero. Note that the acceleration due to gravity near theearth’s surface where the experiment takes place can be taken as 32 ft/s2.(a) Suppose that in addition to the conditions described above, a hammer strikes the mass everyπ/2 seconds starting at t = 0. A delta function with impulse of 1 pound-second models theforce of each blow to the mass. Find the function x(t) for the displacement from equilibrium infeet of the mass at time t in seconds. Express x(t) as a piecewise defined function without the use ofunit step or Heaviside functions and such that in each time window it is a different multiple of the samesinusoidal function.(b) Now assume the same spring-mass…A car wheel with a radius r=0.40 meters rotates at 8 rad/sec. Find the distance travelled in 50 seconds.A rod assembly rotates around the z-axis. The mass C is 10 kg and its initial velocity is 7 m/s. A moment and force both acts as shown in the figure where M = 8t2+5 N.m and F = 60 N. Find the velocity of mass C after 2 seconds.
- I NEED HELP. I know kinetic energy is T=T1 + T2 + T3 and potential energy is V = V1 + V2 + V3. I need working out to solve lagrange equations and find equations of motionsWhen the force F = 2i + 9j + 5k N acts on a spherical body with a mass of 5 kg for 2 seconds, it moves from r1 = 3i - 4j + 5k m to r2 = -4i + 3j + 5k m. (a) Find the work done by the force (b)What is the average mechanical strengthAngular 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…
- 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…Dynamics Question A ball with a mass of .5kg is attached to a 1m string. The string is attached to a post and is free to rotate. The string can be assumed to be weightless and not stretch. The ball is spun around the post in the horizontal plane (so gravity is perpendicular to the string and direction of motion) at a rate of 2π radians per second and that is slowing down by .2 rad/s^2. What is the total acceleration vector and the tension in the string?A point charge q1 = +5.00 micro Coulomb is held fixed in space. From a horizontal distance of 6.00 cm, a small sphere with mass 4.00 x 10-3 kg and charge q2 = +2.00 micro Coulomb is fired toward the fixed charge with an initial speed of 40.0 m/s. Gravity can be neglected. What is the acceleration (in m/s2) of the sphere at the instant when its speed is 25.0 m/s?
- A lightweight drone (1.00 kg) is launched at 800 m high and moves upward at a constant velocity (while ignoring the effects of gravity only on the drone). The balloon, when measured at a horizontal distance from you, is about 1600 m away from you. At the moment when the drone moves, you shoot a bullet (weight =180 g) with an initial velocity of 1009 m/s at a fixed angle α, where sin α=3/5 and cos α= 4/5. (g = 9.8 m/s2) c. What is the upward velocity of the drone?You and a friend are raising a beam, but your friend's rope is too short so you lift him off the ground. At the current time, everything is static. The tension in your cord is 1045.6 N, the mass of the beam is 15 kg, and the mass of your friend is 85 kg. The length of the beam is 4.9 m, d = 3.9 m, theta = 43.5 degrees, phi = 62.5 degrees. If you choose the base of the beam as the origin, and the positive torque direction as counter-clockwise, what is the torque from your cord on the friend+beam system?Zorch, an archenemy of Superman, decides to slow Earth’s rotation to once per 29 h by exerting a force parallel to the equator, opposing the rotation. Superman is not immediately concerned, because he knows Zorch can only exert a force of 4.15 × 107 N. For the purposes calculations in this problem you should treat the Earth as a sphere of uniform density even though it isn't. a. How long, in seconds, must Zorch push with this force to accomplish his goal? (This period gives Superman time to devote to other villains.)