Questionmb A block of mass 3 m can move without friction on a horizontal table. This block is attached to another block of mass by a cord that passes over a frictionless pulley, as shown above. If the masses of the cord and the pulley are negligible, what is the magnitude of the acceleration of the descending block? (A) (B) (C) (D) g
Studdy Solution
STEP 1
1. The block of mass can move without friction on a horizontal table.
2. The block of mass is descending vertically.
3. The cord and pulley are frictionless and have negligible mass.
4. We are tasked with finding the acceleration of the descending block of mass .
5. The acceleration due to gravity is .
STEP 2
1. Analyze the forces acting on each block.
2. Write the equations of motion for each block.
3. Solve the system of equations to find the acceleration.
STEP 3
Analyze the forces acting on each block.
- For the block of mass on the table, the only horizontal force is the tension in the cord.
- For the descending block of mass , the forces are the gravitational force downward and the tension upward.
STEP 4
Write the equations of motion for each block.
- For the block of mass on the table:
$ 3m \cdot a = T
\]
- For the descending block of mass :
$ m \cdot a = mg - T
\]
STEP 5
Solve the system of equations to find the acceleration.
First, solve the equation for the block of mass for :
Substitute into the equation for the descending block:
Combine like terms:
Divide both sides by to solve for :
The magnitude of the acceleration of the descending block is:
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