Two blocks are connected by strings and hung from the ceiling as shown. Tension T1 is 187 N and tension T2 is 78 N. Find the mass of each block.
To find the mass of each block, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the two blocks are connected by strings and are hanging motionless, so we can assume that the acceleration is zero.
Let's denote the mass of one block as m1 and the mass of the other block as m2.
To solve for the masses, we'll need to use the forces acting on each block. Let's examine the forces acting on the first block:
1. The tension T1 is acting upwards.
2. The gravitational force (weight) is acting downwards, which is equal to the mass of the first block multiplied by the acceleration due to gravity (9.8 m/s^2).
Since the block is hanging motionless, the net force acting on it is zero. Therefore, we can set up the following equation:
T1 - m1 * g = 0
Similarly, for the second block, we have:
T2 - m2 * g = 0
Now, we can substitute the given values for T1 (187 N) and T2 (78 N) into the equations:
187 N - m1 * g = 0
78 N - m2 * g = 0
Since the gravitational acceleration (g) is the same for both blocks, we can solve these equations simultaneously to find the masses m1 and m2.
First, rearrange the equations to solve for m1 and m2:
m1 = 187 N / g
m2 = 78 N / g
Now, substitute the value of the gravitational acceleration:
m1 = 187 N / 9.8 m/s^2
m2 = 78 N / 9.8 m/s^2
Calculate the values:
m1 = 19.1 kg
m2 = 8 kg
Therefore, the mass of the first block is 19.1 kg, and the mass of the second block is 8 kg.