Please solve the following 4 problems step by step clearly, please disregard all the little scribbles and marked answers, Im not sure if i got them correct. Thank you so much in advance!!

Problem 1: Consider the sequence shown in Figures la, 1b, and Ic. m = 24 kg a) In the configuration la, the block 1 and block 2 are connected by a spring. The surface on which b) If you now replace the two rods with two new rods of negligible mass (but keeping the rest of the blocks are is frictionless. The spring is compressed to half its natural length. You are asked to the configuration the same as before), what is the new momentum of inertia about point O? calculate the elastic potential energy of this configuration: Option A: 6 kg m Option B: 12 kg m Option C: 0 kg m Option D: 2 kg m Option A: 12.5 Nm Option B: 6.13 Nm Option C: 1.72 Nm Option D: 6.00 Nm b) In figure 1b, the blocks have been released and the spring decompresses freely, pushing the Problem 4: Consider the parabolic shooting shown in Figure 4. It is known that after the initial blocks 1 and 2. Calculate the magnitude of the velocity that the block 1 acquires: firing, the projectile reaches its maximum height after 1 second. Option A: 5.15 mls Option B: 0.60 m/s Option C: 17.5 m/s Option D: 2.5 m/s ( a) You are asked to calculate the kinetic energy at the moment of the shot (point S). I m Option A: 17.17 Nm Option B: 90.21 Nm Option C: 14.44 Nm Option D: 69.55 Nm c) After some time, the block 2 collides (elastically) with the block 3. You are asked to calculate the magnitude of the velocity acquired by the latter after the collision. 19 b) You are also asked to calculate the kinetic energy at the moment of impact with the ground (point B). 2 m 2 mv 2 Option A: 2.5 mls Option B: 0.60 mls Option C: 17.5 mls Option D: 5.15 m/s Option A: 108.75 Nm Option B: 10.2 Nm Option C: 12.4 Nm Option D: 40.7 Nm Problem 2: Two brothers find themselves on a cliff playing with a board, being in equilibrium. While one end of the board is on solid ground, the other is on the void. Each of the brothers is at () Also, calculate the work done by the force of gravity from the time the projectile is at its one end of the board, as shown in Figure 2. maximum height until it hits the ground. 3 m W = Fd Fn= mg m = En Option A: 0 Nm Option B: 110.2 Nm a) You are asked to calculate the normal force on the feet of the brother on the left: Option C: 12.41 Nm Option D: 58.80 Nm Option A: 24 N Option B: 101 N Option C: 130 N Option D: 343 N b) Calculate the work made by gravity W = F- d Figure 1: Option A: 0 Nm Option B: 10 Nm Option C: 100 Nm Option D: 200 Nm M M M Problem 3: Four blocks, each of mass M -6 kg, are arranged on a cross formed by two thin rods of length L = Im and mass M - 6 kg. That is, the mass of each block is equal to the mass of each 1/2 10 rod. [Remember: the momentum of inertia of a thin rod of mass M and length L is / = L'M/12] M =2 kg k = 100 N/m m = 36 a) If the system, which behaves like a solid body rotating about point O, makes 1 revolution per 6. 28 M second, what is the angular momentum about point O? M M Option A: 26.2 kg m'/s Option B: 13.3 kg m/s Option C: 31.1 kg m'/s Option D: 43.9 kg m2/s VI = ? V 2 = 2 . 5 R = - 5m L = I .W I = ( 12 ( 12 kg ) ) 2 - M 3 L = 3. V 12 V1 = 2.5 = 3 V W = 4. 36 m , V 1 = m z Vz R ( 2) ( 2 . 5 ) = 2 ( V 2 )Figure 2: Figure 4: to to max h. At = Is 2 m Cos Im OM =2kg Vo 459 S 3 m. 2 m Figure 3: M 6 ka Im 1,50 Useful formulae: M G Kg M L = IW W = 2nf W = V/R particle = mR2 E = 1/2 mv2 + V V spring = 1/2 k (4x)2 V gravity = mgh 6 Kg W = 1/2 mvp- 1/2 m vi W = Vi-Vf W = AKE W = Fx Ax AX = viAt + 1/2 a ( At) ? L = Mr xv T = rxF F = Ma torque