Question

plm for each time step. Use the approximation that aye A paddle ball toy consists of a flat wooden paddle and a small rubber ball that are attached to each other by an elastic band (figure). You have a paddle ball toy for which the mass of the ball is 0.015 kg, the stiffness of the elastic band is 0.950 N/m, and the relaxed length of the elastic band is 0.330 m. You are holding the paddle so the ball hangs suspended under it, when your cat comes along and bats the ball around, setting it in motion. At a particular instant the momentum of the ball is <-0.02, -0.01, -0.02 kg m/s, and the moving ball is at location-0.2, -0.61, 0> m relative to an origin located at the point where the elastic band is attached to the paddle Part 1 (a) Determine the position of the ball 0.1 s later, using a At of 0.1 s. (Express your answer in vector form.)
Please help wtih all 3!

Answer 1

mass of the ball m = 0.015 kg

string length l = 0.330 m

elastic const. k = 0.95 N/m

momentum of the ball  p = <-0.02,-0.01,-0.02> kg-m/s

position  r = <-0.2,-0.61,0> m

$\Delta$t =0.1 s

average velocities of the ball

v_x = -0.02 m/s ; v_y = -0.01 m/s ; v_z = -0.02 m/s

after 0.1s

x= -0.2 -0.02*0.1 = -0.202 m

y = -0.61 - 0.01*0.1 = -0.611 m

z= 0 -0.02*0.1 = -0.002 m

position at 0.1 s r(0.1) = <-0.202, -0.611, -0.002>

c)

average velocity $\Delta$ r/$\Delta$t = p/m

We only know the final momentum p , we do not know the change in momentum $\Delta$ p and the $\Delta$ t, time interval. We cannot estimate the force and the acceleration. We can only compute the average velocity from the final momentum. Using average velocity, the motion is uniform and it will not make any difference of the size in interval $\Delta$ t , if it is 0.05 s or 0.1 s

The answer will not be different and any arbitrary time step will do.