The 20-kg sphere, attached to a spring of stiffness 500 N/m is released from an un-stretched position of the spring, as shown in the figure. Determine the velocity of the block “A” of mass 10 kg, at the instant the ball has fallen 25 cm. A roller mechanism keeps the spring in a vertical position. Ignore the size of the ball and the mass of the spring and roller mechanism. The coefficient of kinetic friction between the block “A” and the ground is 0.25 Here is an image of the problem: http://s1306.photobucket.com/user/wellthisisdumb/media/1_zps80a2c31a.png.html All angles in the triangle are 60°. I started by making free-body-diagrams for the ball and the block, then I made separate diagrams for the Normal force between the two objects. Here are the diagrams: http://s1306.photobucket.com/user/wellthisisdumb/media/2_zpsf6514a00.png.html I know that as the ball falls, the spring force increases, so the effect of the ball on the block's movement will decrease with distance, so I know I need an equation for motion of the block in terms of x(the displacement of the ball). Wb = Weight of Ball(B) Wa = weight of block A Fs = spring force Ff = frictional force Na = Normal force of A Nb = Normal force of B Wb = mg = 20(9.8) = 196N Wa = mg = 10(9.8) = 98N Fs = 500(.25) = 125 N Nb = Wb - Fs = 196 - 500x Na = Wby + Wa = Nbsin60 + 98 = (196 - 500x)sin60 +98 = 267.7 - 433x Wbx = Nbcos30 = (196 - 500x)cos30 = 169.7 - 433x Ff = μNa = .25(267.7 - 433x) = 66.9 - 108x ƩFx = Wbx - Ff = MaAx (169.7 -433x) - (66.9 - 108x) = 10Ax 102.8 - 325x = 10Ax 10.28 - 32.5x = Ax I have my equation for the acceleration of the block in terms of the motion of the ball, so next I used ads = vdv to solve for velocity ads = vdv ∫ads = ∫vdv (ads from 0 to .25, vdv from 0 to V) ∫(10.28 - 32.5x)dx = 1/2(v^2) 10.28x - 16.25x^2 = 1/2(v^2) 10.28(.25) - 16.25(.25)^2 = 1/2(v^2) 1.55 = 1/2(v^2) 3.1 = v^2 1.76 m/s = v So I got v = 1.76 m/s as my answer. My professor said to use ads = vdv to solve the problem, and this is the only way that I could get to even using ads = vdv. I feel like I've done it correctly, but we've never done a problem even similar to this in class, so I'm just kind of lost. If someone could verify that I got the right answer that would be great, and if it's wrong I'd really appreciate a step-by-step solution. Thank you!