A 20N block rests on a table, connected by a massless rope to a 12N block hanging off the table. Assume the pulley is light and frictionless.
What is the tension in the rope?
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I calculated the masses to be 2.04kg and 1.22kg respectively. From there, the free-body diagram for the 12N block (block 2) suggested to me that using Newton's 2nd Law would yield:
Fnet = ma
T + W2 = (m1 + m2)g
T = (m1 + m2)g - W2
T = (3.265)(9.81)-12
T = 20N
But this is not correct. I believe the correct answer is 7.50N but I do not understand how to calculate that. What am I missing? Thanks
What is missing, is that the block on a table is moving, and the table is frictionless. So the 12N block is pulling the larger block
at the smaller block
tension=m(g-a)
at the large block
tension=Ma
Ma=mg-ma
a(M+m)=mg
a=mg/(M+m)
now you can solve for tension in either equation
For the smaller block, wouldn't the sum of forces be:
T - W = ma
T - mg = ma
T = ma + mg = m(a+g)
Why is it m(g-a) instead?
nope, if if it were falling free fall, a=g
tension=m(g-a)=zero Think that out.
Ok, thanks
To find the tension in the rope, you need to consider both blocks and their respective forces.
Let's start by analyzing the forces acting on Block 1 (the 20N block resting on the table). The only force acting on it is its weight, which is equal to its mass (m1) multiplied by the acceleration due to gravity (g). So, the weight of Block 1 is 20N.
Now let's look at Block 2 (the 12N block hanging off the table). Again, the only force acting on it is its weight, which is equal to its mass (m2) multiplied by the acceleration due to gravity (g). So, the weight of Block 2 is 12N.
Since the blocks are connected by a rope that passes over a pulley, they experience the same tension force. The tension force is the force transmitted through the rope and it is the same on both sides of the pulley.
Therefore, the tension force (T) in the rope is equal to the weight of both blocks combined. We can calculate it as:
T = Weight of Block 1 + Weight of Block 2
T = m1 * g + m2 * g
Using the masses you provided (m1 = 2.04 kg and m2 = 1.22 kg) and the acceleration due to gravity (g = 9.81 m/s²), we can calculate the tension force:
T = (2.04 kg) * (9.81 m/s²) + (1.22 kg) * (9.81 m/s²)
T = 20 N
So, the correct tension force in the rope is indeed 20N, not 7.50N as you mentioned earlier. It seems there was an error in calculating the masses or the weights of the blocks.