Use the approximation that vavg = pf/m for each time step. A paddle ball toy con

Question

Use the approximation that vavg = pf/m for each time step. 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 0.014 kg, the stiffness of the elastic band is 0.880 N/m, and the relaxed length of the elastic band is 0.320 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.

(a) Determine the position of the ball 0.1 s later, using a ?t of 0.1 s. (Express your answer in vector form.) r =

(b) Starting with the same initial position ?0.2, ?0.61, 0 m and momentum ?0.02, ?0.01, ?0.02 kg · m/s , determine the position of the ball 0.1 s later, using a ?t of 0.05 s. (Express your answer in vector form.) r =

TA gave me the equation and I still can't solve it .. use it

Explanation / Answer

Initial momentum P(initial) = -0.02i - 0.01j - 0.02k

Initial position = r (initial) = -0.2i - 0.61j + 0k    modulus(r initial) = sqrt( (-0.2)^2 + (-0.6)^2) = 0.632m

mass = 0.014 kg L0 = 0.32

k = 0.88N/m

From above equation F net = - 0.014*9.8 j - 0.88 *(0.632 -0.32) (-0.2i - 0.61j + 0k ) /0.632

= -0.1372j - 0.4344  (-0.2i - 0.61j + 0k ) = 0.868i + 0.1278j

now p( final) = P( initial ) + F net ( delta t)   So p( final) = -0.02i - 0.01j - 0.02k + (0.868i + 0.1278j)* 0.1

  p( final) = -0.02i - 0.01j - 0.02k + (0.868i + 0.1278j)* 0.1 = 0.668 i +0.00278 j -0.02 k

now V (avg) =   (0.668 i +0.00278 j -0.02 k) / 0.014 = 4.78 i + 0.1985j -1.428k

r ( final) = r (initial) + v(avg) * ( delta t)

So R final = -0.2i - 0.61j + 0k + ( 4.78 i + 0.1985j -1.428k) * 0.1

= 0.278 i -0.58015 j -0.1428 k

Similarly we have to do this for delta t = 0.5 seconds as well.

So F net remains the same from above calculations. Since r ( initial) and L 0 are same

SO Fnet = 0.868i + 0.1278j

p (final) = P ( initial) + F net ( delta t)   So p( final) = -0.02i - 0.01j - 0.02k + (0.868i + 0.1278j)* 0.05

From p final we can calculate v (average ) and finally r final.

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