Tension, mass, and velocity

[Gear2d]

Homework Statement

I have a 12kg block that is raised by a rope. If the velocity of the mass is decreasing at a rate of 5 m/s^2, what is tension in the rope?

Homework Equations

T=mg
F=ma

The Attempt at a Solution

My solution: T = mg+ ma = 180N

Book solution: T+ma = mg => 60N

I am confused as why you are subtracting here. I see that acceleration is in the downward direction (as stated by the question stem), but the object is still been raised. So shouldn't it be T = mg+ ma? Because to me, T+ma =mg looks like that acceleration of the mass is the upward direction (if that were the case the object would be increasing it speed not decreasing),

 

[alphysicist]

Hi Gear2d,

Homework Statement

I have a 12kg block that is raised by a rope. If the velocity of the mass is decreasing at a rate of 5 m/s^2, what is tension in the rope?

Homework Equations

T=mg

This equation is not true.

F=ma

I think you might need to be a bit more careful with this equation. This equation should be either:

$$\sum \vec F = m \vec a \mbox{ or } \vec F_{\rm net} = m\vec a$$

and when you actually use it here, for example in the $y$ direction, you get:

$$\begin{align} \sum F_y = m a_y\nonumber\\ F_{1y}+F_{2y} = m a_y\nonumber \end{align}$$

since there are two forces. So what are the $y$-components, including sign, of the tension and weight forces? And what is the $y$-component of the acceleration? Those, with the correct sign, are what go into the force equation.

The Attempt at a Solution

My solution: T = mg+ ma = 180N

Book solution: T+ma = mg => 60N

I am confused as why you are subtracting here. I see that acceleration is in the downward direction (as stated by the question stem), but the object is still been raised. So shouldn't it be T = mg+ ma? Because to me, T+ma =mg looks like that acceleration of the mass is the upward direction (if that were the case the object would be increasing it speed not decreasing),

 

[baba89]

and the tension and gravity are in the downward direction.



Your solution is correct. The book solution seems to have made a mistake in assuming that the acceleration is acting in the upward direction, which is not the case as stated in the question. The correct equation to use in this scenario would be T = mg + ma, where m is the mass of the block, g is the gravitational acceleration, and a is the acceleration in the downward direction. It is important to pay attention to the direction of acceleration in order to correctly determine the tension in the rope. Keep up the good work!