Two blocks sit on a horizontal surface. They are connected to each other by a massless cord. The block on the left has a mass of 4.8 kg and the block on the right has a mass of 2.2 kg. Another massless cord is attached to the block on the right and pulls that block with a horizontal force of 49 N causing both blocks to accelerate at a rate of 1.1 m/s2 to the right. The block on the right has a frictional force of 14 N opposing the motion.
a) What is the frictional force opposing the motion for the block on the left?
b) What is the tension in the cord connecting the two blocks?
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To find the frictional force opposing the motion for the block on the left (a), we can use Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration.
We know that the acceleration of both blocks is 1.1 m/s² to the right. The mass of the block on the left is 4.8 kg. Therefore, the net force on the block on the left can be found using the formula:
Net Force = Mass × Acceleration
Net Force = 4.8 kg × 1.1 m/s²
Net Force = 5.28 N
Since the only other force acting on the block on the left is friction, we can conclude that the frictional force opposing the motion for the block on the left is 5.28 N (b).
To find the tension in the cord connecting the two blocks (c), we need to consider both blocks as a system and apply Newton's second law again.
The net force acting on the system is given by the force applied to the block on the right minus the frictional force acting on the block on the right:
Net Force = Force Applied - Frictional Force
Net Force = 49 N - 14 N
Net Force = 35 N
Since the blocks are connected by a massless cord, the tension in the cord is the same throughout the cord. Therefore, the tension in the cord connecting the two blocks is equal to the net force acting on the system:
Tension = Net Force
Tension = 35 N (d)