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3. Refer to the diagram, which shows an overhead view of four point masses connected by...

Question:

3. Refer to the diagram, which shows an overhead view of four point masses connected by two massless rods that intersect each other at right angles (Overhead View) The masses and distances are as follows: m,-1.56 kg m2-3.87kg m, -2.94 kg m, 4.68 kg dı = 2.30 m d2 = 1.75 m d,-0.9 12 m 4-3.40 m This rigid structure is lying flat, initially at rest in the position shown, ona frictionless surface. It is pinned to that surface at the rods intersection point The structure can rotate about the (frictionless) pin, but the pin doesnt move. Let an x-y coordinate system be defined with its origin at the pin (pin) Throughout the time interval 0sts5.30 s, a counter-clockwise torque is applied to the structure. This torque varies with time: t(t) - A B, where 1 is measured in seconds. A 6.87 N·m/s2/3, and B 0.654 N·m The torque is removed (becomes zero) at t-5.30 s. Im Att- 9.78 s, the pin is removed (frictionlessly-pulled straight up), so that the entire rigid structure is then free to move on the frictionless surface. Calculate the location (x- and y- coordinates) of the rods intersection point at t 12.0s.

3. Refer to the diagram, which shows an overhead view of four point masses connected by two massless rods that intersect each other at right angles (Overhead View) The masses and distances are as follows: m,-1.56 kg m2-3.87kg m, -2.94 kg m, 4.68 kg dı = 2.30 m d2 = 1.75 m d,-0.9 12 m 4-3.40 m This rigid structure is lying flat, initially at rest in the position shown, ona frictionless surface. It is pinned to that surface at the rods' intersection point The structure can rotate about the (frictionless) pin, but the pin doesn't move. Let an x-y coordinate system be defined with its origin at the pin (pin) Throughout the time interval 0sts5.30 s, a counter-clockwise torque is applied to the structure. This torque varies with time: t(t) - A B, where 1 is measured in seconds. A 6.87 N·m/s2/3, and B 0.654 N·m The torque is removed (becomes zero) at t-5.30 s. Im Att- 9.78 s, the pin is removed (frictionlessly-pulled straight up), so that the entire rigid structure is then free to move on the frictionless surface. Calculate the location (x- and y- coordinates) of the rods' intersection point at t 12.0s.

Answers

The moment of inertia of the system about the pin is given as follows: 1 md? +m,d?+m,d? +m,d? (1.56 kg) (2.30 m) +(3.87 kg)(1Velocity of mass m (directed along positive x-direction) is given as follows: (0.912 m) (0.91 16) 0.813 m/s Velocity of mass

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The total moment of inertia of all masses about the pin point is 1-т,d? + m,a; + m, а; +m,d? 1.56kg)(2.30 m +(3.87kg )(1.75m)Integrating the above expression on both sides 5.30s (4i+B)di 2/3 + В ) dt 0 do= I 0 5.30s ((6.87N-m/3/) 4N-m))dt (0.654N 0 7(m,) in x-direction is The linear velocity of the mass = (2.30m)(0.9116rad/s) =2.097m/s The linear velocity of the mass (m2)The linear velocity of masses m, and mg are in opposite direction so the total velocity along x-direction can be determine asThe distance travelled by the pin in x -direction after pin removed is =(-1.266m/s)(2.22s) -2.81m x is x-coordinate of the pi

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