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 5.1 kg and the block on the right has a mass of 3.0 kg. Another massless cord is attached to the block on the right and pulls that block with a horizontal force of 48 N causing both blocks to accelerate at a rate of 1.6 m/s2 to the right. The block on the right has a frictional force of 12 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?
To solve this problem, we'll first need to determine the net force acting on each block. Then, using Newton's second law of motion (F = ma), we can find the frictional force opposing the motion for the block on the left and the tension in the cord connecting the two blocks.
Let's start with the block on the right.
1) Net force acting on the block on the right:
The force applied by the external cord is 48 N, and the frictional force opposing the motion is 12 N. Since the blocks are accelerating to the right, the net force is the vector sum of these two forces: F_net = 48 N - 12 N = 36 N.
2) Mass of the block on the right:
Given that the mass of the block on the right is 3.0 kg.
3) Acceleration of the system:
The given acceleration value of 1.6 m/s^2 is the acceleration of the entire system, which includes both blocks. Since the blocks are connected, they have the same acceleration.
Now, let's move on to the block on the left.
4) Mass of the block on the left:
Given that the mass of the block on the left is 5.1 kg.
5) Frictional force opposing the motion for the block on the left:
We know that the net force acting on the block on the left is equal to the frictional force opposing the motion. Using Newton's second law, F = ma, we can rearrange the equation to solve for the frictional force: F = ma. Thus, the frictional force opposing the motion for the block on the left is equal to the mass of the block on the left multiplied by its acceleration: F_friction_left = m_left * a.
6) Tension in the cord connecting the two blocks:
The tension in the cord is the force pulling the block on the left forward. Since the block on the right experiences a net force, there must be an equal and opposite net force on the block on the left due to the tension in the cord. Therefore, the tension in the cord is equal to the net force on the block on the left: Tension = F_net_left.
Finally, let's calculate the answers to the given questions:
a) Frictional force opposing the motion for the block on the left (F_friction_left):
F_friction_left = m_left * a = 5.1 kg * 1.6 m/s^2 = 8.16 N.
b) Tension in the cord connecting the two blocks (Tension):
Tension = F_net_left = F_friction_left = 8.16 N.
Therefore, the frictional force opposing the motion for the block on the left is 8.16 N, and the tension in the cord connecting the two blocks is 8.16 N as well.