Calculating Tension in a Falling 5kg Brick on a Rope | Homework Problem

[demonslayer42]

Homework Statement

A 5kg brick on a rope is lowered towards the ground. While the brick is accelerating downward at 1.5m/s^2, find the tension in the rope. What is the reaction force to the upward force of tension acting on the brick?

Homework Equations

Sum of F = ma
w = Fg = mg
g = 9.8 m/s^2

The Attempt at a Solution

So basically what I did was drew a diagram.

/\ T
#
#
# a = -9,8 m/s^2
#
#
\/ W = mg = 5.0(9.8) = 49 N

T = mg + ma = 49 + 5.0(-1.5) = 41.5 N

O.k. where did i go wrong? lol I can't figure this out and it's driving me crazy

 

[PhanthomJay]

Doesn't look wrong to me...why do you think it is wrong?

 

[demonslayer42]

Because I always do something wrong...You sure it's correct? I'm just really shocked I got it correct it seems to easy i must be missing something.

 

[PhanthomJay]

You noted correctly that T=mg + ma, where a is negative. How did you arrive at that equation? That's the most important part.

 

[rwisz]

Your approach is correct, but there is a small mistake in your calculation. The equation T = mg + ma is the correct way to find the tension in the rope. However, when plugging in the values, you forgot to include the negative sign for the acceleration (-1.5m/s^2).

The correct calculation should be T = mg + ma = 49 + 5.0(-1.5) = 49 - 7.5 = 41.5 N.

The reaction force to the upward force of tension acting on the brick is equal in magnitude but opposite in direction, so it would also be 41.5 N. This is known as Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.

Overall, your approach was correct, but just be mindful of including all the necessary signs in your calculations. Keep up the good work!