In the drawing, the weight of the block on the table is 380 N and that of the hanging block is
175 N. Ignore all frictional effects, and assuming the pulley to be massless. What is the
acceleration of the two block?
m₁g+m₂g =(m₁+m₂)g =380+175=555
(m₁+m₂) =555/g=56.6 kg
m₁a =T
m₂a=-T+m₂g
m₂a = - m₁a +m₂g
a=(m₂g)/(m₁+m₂) =
=175/56.6=3.1 m/s²
To determine the acceleration of the two blocks, we need to apply Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
First, let's understand the forces acting on each block:
1. Block on the table (380 N):
- Weight (mg): The weight of the block is acting downward, equal to its mass multiplied by the acceleration due to gravity (9.8 m/s² in most cases, but let's assume it's given in the problem).
- Tension in the rope: There is tension in the rope pulling the block. We'll label it T.
2. Hanging block (175 N):
- Weight (mg): The weight of the hanging block is acting downward, equal to its mass multiplied by the acceleration due to gravity.
- Tension in the rope: The tension in the rope is acting upward, pulling the hanging block. We'll also label it T.
Since the pulley is assumed to be massless, the tension on both sides of the rope is equal. Therefore, the tension in the rope pulling the block on the table is the same as the tension pulling the hanging block.
Now, let's set up the equations of motion for each block:
For the block on the table:
- Sum of the forces in the vertical direction: T - mg = ma₁
For the hanging block:
- Sum of the forces in the vertical direction: T - mg = ma₂
Since we're interested in the acceleration of the system as a whole, we can eliminate the tension term (T) when combining the equations:
ma₁ = T - mg
ma₂ = mg - T
Now, solve for the acceleration:
Combine the two equations:
ma₂ + ma₁ = (mg - T) + (T - mg)
ma₁ + ma₂ = 0
Simplify:
a₁(m₁ + m₂) = 0
Since the mass of the two blocks is given and positive, we can conclude that the acceleration of the system is zero.
Therefore, the acceleration of the two blocks in this scenario is 0 m/s².