A 2.13-kg object on a frictionless horizontal track is attached to the end of a horizontal spring whose force constant is 5.00 N/m. The object is displaced 3.54 m to the right from its equilibrium position and then released, initiating simple harmonic motion. (a) What is the force (magnitude and direction) acting on the object 3.50 s after it is released

Atotal charge of –6.50 µc is uniformly distributed within a sphere that has a radius of 0.150 m. what is the magnitude and direction of the electric field at 0.300 m from the surface of the sphere? a) 2.89 × 105 n/c, radially inward b) 6.49 × 105 n/c, radially outward c) 4.69 × 105 n/c, radially inward d) 9.38 × 105 n/c, radially outward e) 1.30 × 106 n/c, radially inward

Which statement is true? a. kepler's laws apply only to the motion of earth. b. kepler's laws can be used to predict eclipses. c. kepler's laws are true for a central force that is directly proportional to distance. d. kepler's laws can be deduced from newton's laws of motion and gravity.

5submission this assignment is worth 20 points total. you are required to submit the following by next lab: 1. (3 points) determine the equation for the output angular velocity ω2 = θ˙ 2 as a function of θ1, ω1 = θ˙ 1 and α. you must show all your work to receive credit. 2. (2 points) use the result of problem#1 to plot ω2 over 0 ≤ θ1 ≤ 360deg with ω1 = 360deg/sec. do this for α = {10,30}deg. show the results on the same plot and properly label the axes, title, legend. for this you can use matlab or ms excel. 3. (3 points) determine the equation for the output angular acceleration ω˙ 2 and create a plot similar to the one in problem#2. 4. (10 points) submit plots of the results (ω2 and ω˙ 2) obtained from creo/mechanism and compare them to results of problem#2 and problem#3. note that you should do these comparisons for the two cases with α = {10,30}deg. 5. (2 points) provide a brief explanation of the results. did they match? what are the implications as misalignment angle increases?