Three blocks are located on a horizontal frictionless table. They are connected by a massless cord, as shown in the figure, and pulled to the right. The masses of the three blocks are m1 = 45 kg, m2 = 39 kg, and m3 = 50 kg. The pulling force is equal to T3 = 46 N.
46 = (45 + 39 + 50) a
solve for a
then force on block 1
= 46 - (39+50) a
etc
To find the acceleration of the system, we need to analyze the forces acting on each block.
First, let's consider block 3. The pulling force T3 is acting to the right on block 3. The tension in the cord is the same throughout, so the force acting on block 2 is also T3.
Next, let's consider block 2. In addition to the tension force T3 acting to the right, block 2 experiences a tension force T2 acting to the left from block 1. The net force on block 2 can be calculated as the difference between the two tension forces:
Net force on block 2 = T3 - T2
Finally, let's consider block 1. Block 1 is experiencing a tension force T1 acting to the left from block 2. Therefore, the net force on block 1 can be calculated as:
Net force on block 1 = T2 - T1
Since the table is frictionless, the only external force acting on the system is the pulling force T3. Therefore, the net force on the system is equal to T3.
Now, we can set up a system of equations using Newton's second law (F = ma) for each block:
m3 * a = T3 (1)
m2 * a = T3 - T2 (2)
m1 * a = T2 - T1 (3)
Rearranging equation (2), we can solve for T2:
T2 = T3 - m2 * a (4)
Substituting equation (4) into equation (3), we can solve for T1:
m1 * a = (T3 - m2 * a) - T1 (5)
Simplifying equation (5), we get:
T1 = T3 - (m1 + m2) * a (6)
Substituting equations (4) and (6) back into equation (1), we can solve for the acceleration a:
m3 * a = T3
Substituting T2 = T3 - m2 * a and T1 = T3 - (m1 + m2) * a:
m3 * a = T3
m3 * a = (T3 - m2 * a)
m3 * a = (T3 - m2 * a) - (T3 - (m1 + m2) * a)
Simplifying:
m3 * a = (m1 + m2) * a
Canceling the acceleration on both sides:
m3 = m1 + m2
Substituting the given masses:
50 kg = 45 kg + 39 kg
Simplifying:
50 kg ≠ 84 kg
Since the equation is not satisfied, there seems to be a mistake in the given problem. Please check the masses or the equation provided.