two blocks of mass M kg and 2.5 kg respectively are connected by a light inextensible string the string runs over a light frictionsless pulley the blocks are stationary. calculate the tension in the string
Why did the string go to therapy? It was feeling a little tense.
But in all seriousness, let's calculate the tension in the string for this scenario. Since the blocks are stationary, the tension in the string will be equal to the weight of the blocks. The weight of an object is given by the formula:
Weight = mass x acceleration due to gravity
For the first block, the weight is Mg, where M is the mass of the block. For the second block, the weight is 2.5g. Since the blocks are connected by a string, the tension in the string is the same for both blocks.
So, the tension in the string is:
Tension = Weight of block 1 = Weight of block 2
Tension = Mg = 2.5g
Now we can substitute the value of acceleration due to gravity, which is approximately 9.8 m/s^2, to find the tension:
Tension = M x 9.8 = 2.5 x 9.8
So, the tension in the string is equal to 9.8M Newtons.
To calculate the tension in the string, we can use Newton's second law and the principle of conservation of energy.
First, let's consider the forces acting on the two blocks:
1. Block 1 (mass = M kg):
- Weight (downward force) = M * g (where g is the acceleration due to gravity)
- Tension in the string (upward force)
2. Block 2 (mass = 2.5 kg):
- Weight (downward force) = 2.5 * g
- Tension in the string (downward force)
Since the blocks are stationary, the net force on each block must be zero. Therefore:
For Block 1:
Tension - M * g = 0 ... (Equation 1)
For Block 2:
2.5 * g - Tension = 0 ... (Equation 2)
To find the tension, we can solve these two equations simultaneously.
From Equation 1, we can write:
Tension = M * g
Substituting this into Equation 2:
2.5 * g - M * g = 0
Simplifying, we have:
2.5 * g = M * g
Canceling the g terms, we get:
2.5 = M
Therefore, the tension in the string is M * g = 2.5 * g.
To calculate the tension in the string, we need to determine the forces acting on each block.
First, let's consider the block with mass M kg. The force acting on it is its weight, which is given by the equation:
Weight = mass x gravitational acceleration
Weight = M x 9.8 (N)
Since the block is stationary, the tension in the string is equal to the weight of this block. So, the tension in the string when considering the block with mass M kg is also M x 9.8 (N).
Next, let's consider the block with mass 2.5 kg. The tension in the string is also acting on this block. We know that the net force on this block is equal to the product of its mass and acceleration (F = m x a). However, since the block is stationary, the net force on it is zero. Therefore, we have:
Tension in the string - Weight = 0
Tension in the string = Weight
Tension in the string = 2.5 x 9.8 (N)
So, the tension in the string is M x 9.8 N for the block with mass M kg, and 2.5 x 9.8 N for the block with mass 2.5 kg.