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An object of mass m moving under the action of a central force Fc(r) due to a much bigger object of mass M. i. Define a central force Fc (r). ii. Write the areal velocity A˙ in terms of the mass m and magnitude L of the angular momentum of the smaller object. iii. Show that the Kepler’s third law (the harmonic law) actually can be deduced from your answer in part a) ii.
A particle of mass m = 100 g is attached on both sides to a pair of light springs along each of the Cartesian coordinate axis; x-, y- and z-axis. The spring each has a different spring constant kx, ky and kz along the x-, y- and z-axis respectively. In all cases, neglect the effects of weight and resistance on the particle. a) At some instant of time, the particle is located at position r = x^ i +y ^ j+z ^k from the equilibrium point. i. Write the expression for the net force F (x ,y , z) acting on the particle. ii. Write the components of the equation of motion (EOM) for the particle. iii. Write the general solutions to the equations in part ii. above.
Consider a system with a damping force undergoing forced oscillations at an angular frequency omega
Find the instantaneous kinetic and potential energy of the system.
Find the degrees of freedom for dumbbell moving in space then how to calculate
How to find out degrees of freedom?
Blocks A and B have weights of 44 N and 22 N, respectively. (a) Determine the minimum weight of block C to keep A from sliding if between A and the table is 0.20. (b) Block C suddenly is lifted off A. What is the acceleration of block A if 3 between A and the table is 0.15?
A 10 kg monkey climbs up a massless rope that runs over a frictionless tree limb and back down to a 15 kg package on the ground. (a) What is the magnitude of the least acceleration the monkey must have if it is to lift the package off the ground? If, after the package has been lifted, the monkey stops its climb and holds onto the rope, what are the (b) magnitude and (c) direction of the monkey’s acceleration and (d) the tension in the rope?
If a bullet leaves the muzzle of a rifle with a speed of 580. m/s and accelerates at a rate of 1.9 x 105 m/s2, how long is the barrel of the rifle?
A baseball pitcher throws a fastball at a speed of 40.25 m/s (90. mph). The acceleration occurs as the pitcher holds the ball in his hand and moves through an almost straight-line distance of 3.40 m. Assuming that the acceleration is uniform, determine the acceleration. Compare the acceleration to the acceleration due to gravity (ratio or ‘G force’).
Hans has a mass of 100kg and Franz has a mass of 50kg. Who will stretch the bungee cord by a longer length?
