In the drawing, the weight of the block on th
e 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?
To find the acceleration of the two blocks, we can use 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. In this case, we need to consider two blocks: the block on the table and the hanging block.
Let's define the acceleration of the two blocks as a. Since the blocks are connected by a rope passing over a pulley, we can assume that the acceleration of both blocks is the same.
To begin, we need to find the net force acting on each block. For the block on the table, the net force is equal to the weight of the block minus any force opposing its motion. Since there is no friction, the net force acting on the block on the table is simply its weight:
Net force on block on table = Weight of block on table = 380 N
For the hanging block, the net force is the difference between its weight and the tension in the rope:
Net force on hanging block = Weight of hanging block - Tension in the rope
The tension in the rope is equal to the force required to accelerate the block, so:
Net force on hanging block = Weight of hanging block - Tension in the rope = Weight of hanging block - (mass of hanging block × acceleration)
From the problem statement, we know that the weight of the hanging block is 175 N. Let's call the mass of the hanging block m. Since the net force on both blocks is the same, we can now set up an equation:
380 N = 175 N - (m × a)
Solving for a:
380 N + (m × a) = 175 N
(m × a) = 175 N - 380 N
(m × a) = -205 N
a = -205 N / m
Therefore, the acceleration of the two blocks is -205 N / m. Since the mass of the hanging block (m) is not given in the question, we don't have enough information to find the exact value of the acceleration.