Blocks connected on a table - find acceleration and tension

In summary, the problem involves three blocks connected on a rough table with frictionless pulleys. The goal is to determine the magnitude of acceleration for each block and the tension in the two cords. Using the equation F=ma, the solution involves setting up equations for each block and solving for acceleration, tension, and friction. The final answer is a=2.31, T1=29.96, and T2=24.32 (or 24.22) N.
  • #1
blackboy
61
0

Homework Statement


Blocks.jpg

Three blocks are connected on a table as shown in Figure P5.50. The table is rough and has a coefficient of kinetic friction of 0.350. The pulleys are frictionless.

Determine the magnitude of acceleration of each block.

Determine the tension in the two cords.


Homework Equations


F=ma


The Attempt at a Solution


I was thinking that everything accelerates the same magnitude. If so
4g-T1=4a
T1-T2-f=a
T2-2g=2a

Then solving I get a=2.31, T1=29.96, T2=24.32.
I am not sure if this is the right answer, because the problem hints that the accelerations aren't equal. If they aren't equal, can someone show me how to do this?
 
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  • #2


I didn't check your arithmetic, but your equations are fine. (Everything accelerates together.)
 
  • #3


Looks like a typo for T2. It's close to, but not exactly 24.32 N.
 
  • #4


24.22N. Sorry.
 
  • #5


Looks good to me! :smile:
 

FAQ: Blocks connected on a table - find acceleration and tension

How do you find the acceleration of blocks connected on a table?

The acceleration of blocks connected on a table can be found by using Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration. By analyzing the forces acting on the blocks, such as gravitational force and tension, the acceleration can be calculated.

What factors affect the acceleration of blocks connected on a table?

The acceleration of blocks connected on a table can be affected by various factors, such as the mass and weight of the blocks, the angle of the incline or slope of the table, and the coefficient of friction between the blocks and the table. The presence of external forces, such as air resistance, can also affect the acceleration.

How can you calculate the tension in the string connecting the blocks?

The tension in the string connecting the blocks can be calculated using the equation T = m1a + m1g + m2a, where T is the tension, m1 and m2 are the masses of the blocks, a is the acceleration, and g is the gravitational acceleration. This equation takes into account the forces acting on the blocks and the string, such as the weight of the blocks and the tension force itself.

What is the relationship between the tension and acceleration of blocks connected on a table?

The tension and acceleration of blocks connected on a table have an inverse relationship. This means that as the tension in the string increases, the acceleration of the blocks decreases, and vice versa. This can be explained by Newton's second law, as the net force on the blocks decreases as the tension increases, resulting in a smaller acceleration.

Can the acceleration and tension of blocks connected on a table ever be equal?

Yes, it is possible for the acceleration and tension of blocks connected on a table to be equal in certain scenarios. This can occur when the net force on the blocks is zero, meaning that the forces acting on the blocks are balanced. In this case, the acceleration and tension would be equal and the blocks would remain in a state of equilibrium on the table.

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