14.2 : 単一粒子の線形力積と運動量の原理: 問題解決

Consider a massless pulley system consisting of a wooden box and a cylinder of known masses. Determine the speed of the attached objects at a specific time after the system is released from rest.

For the analysis, establish an appropriate coordinate system to determine the length of the entire rope. The time derivative of this length equation gives the velocity equation.

Draw a free-body diagram for the cylinder, indicating its weight and the tension in the rope. Apply the principle of linear impulse and momentum to the cylinder.

Here, the initial momentum is zero, while the impulse is due to the weight of the cylinder and the tension on the rope.

Similarly, draw a free-body diagram for the wooden box, indicating all the forces acting on it. Apply the principle of impulse and momentum and substitute the known values to simplify the equation.

Now, solve the three equations simultaneously to obtain the unknown velocities.

Assuming the downward velocity as positive, the negative velocity of the wooden box indicates an upward motion of the box.