Question

Cube A is suspended by a string that passes over an ideal pulley and is tied to cube B, which is on a level horizontal frictionless table, as shown. Engineers are to determine the mass of cube B from the motion of the two-cube system after it is released from rest.They plan to measure the time cube A takes to reach the floor.The engineers must also take which of the following measurements to determine the mass of cube B?Question 7 options:The length of the string and the distance cube A falls to reach the floorThe mass of cube A and the distance cube A falls to reach the floorOnly the mass of cube AOnly the distance cube A falls to reach the floorOnly the length of the stringThe mass of cube A and the length of the string

Answer 1

ANSWER:

The correct answer is 2nd option: The mass of cube A and the distance cube A falls to reach the floor

STEP-BY-STEP EXPLANATION:

Final velocity for cube A after reaching on floor its equal to 0 (v = 0)

The change in potential energy provides kinetic energy for the motion of cube B, therefore:

$\begin{gathered} PE=M_A\cdot g\cdot h \\ \\ \frac{1}{2}M_B(v)^2=\frac{1}{2}M_B(u)^2 \end{gathered}$

The value of v as mentioned above is equal to 0, therefore we must calculate the value u, using the following formula:

$\begin{gathered} h=\frac{-u}{2g} \\ \\ u=(-h\cdot2g) \end{gathered}$

So we would finally be left with the following equation:

$M_A\cdot g\cdot h=\frac{1}{2}\cdot M_B(-h\cdot2g)^2$

This means that if we know the mass of A and the distance cube A falls to reach the floor, we can calculate the mass of cube B.

The correct answer is 2nd option: The mass of cube A and the distance cube A falls to reach the floor