In the drawing, the weight of the block on the table is 384 N and that of the hanging block is 195 N. Ignore all frictional effects, and assuming the pulley to be massless.
(a) Find the acceleration of the two blocks.
m/s2
(b) Find the tension in the cord.
To find the acceleration of the two blocks, we need to use Newton's second law of motion, which states that the sum of all forces acting on an object is equal to its mass multiplied by its acceleration (F = ma).
(a) Let's consider the two blocks separately.
The block on the table:
The weight of the block on the table is 384 N, but since there are no other vertical forces acting on it, it cancels out. So, the net force on the block on the table is zero.
Thus, the tension force in the cord is the only horizontal force acting on the block.
Using Newton's second law for the block on the table, we have:
Tension force = mass of the block on the table × acceleration
384 N = mass of the block on the table × acceleration
The hanging block:
The weight of the hanging block is 195 N. Since it is hanging freely, the tension in the cord is equal to its weight.
Tension force in the cord = 195 N
Since the two blocks are connected by the same cord, they have the same acceleration.
Now, we have enough information to solve for the acceleration of the blocks.
The next step is to calculate the mass of the block on the table. To do this, we can use the formula:
mass = weight / gravitational acceleration
Let's assume the gravitational acceleration is approximately 9.8 m/s².
For the block on the table:
mass of the block on the table = 384 N / 9.8 m/s²
Now we can substitute the known values into the first equation to find the acceleration:
384 N = (mass of the block on the table) × acceleration
384 N = (384 N / 9.8 m/s²) × acceleration
Solving for acceleration gives us:
acceleration = 384 N / (mass of the block on the table)
(b) To find the tension in the cord, we can use the equation Tension force = mass × acceleration:
For the hanging block:
Tension force in the cord = mass of the hanging block × acceleration
Now, we can substitute the known values to find the tension in the cord:
Tension force in the cord = (mass of the hanging block) × acceleration
Remember to calculate the mass of the hanging block using the formula:
mass = weight / gravitational acceleration
After calculating the mass, you can substitute the values into the equation to find the tension in the cord.