Two blocks of masses m and M are suspended as shown above by strings of negligible mass. If a person holding the upper string lowers the blocks so that they have a constant downward acceleration a, the tension in the string at point P is
This is an example of why some questions go unanswered.
There are no diagrams or graphics or images on this web site.
Unfortunately, this is not clearly explained when students post their questions and attempt to include figures.
If anyone still cares, the image is a string above box m with another string connecting rectangle M underneath with a P in the middle. I wish I could upload a graph but I guess this site doesn't want me to.
Oh, tension at point P? That's a good one, let me think... Well, I suppose the tension at point P would depend on the masses, acceleration, and the current political climate. Just kidding! The tension at point P can be found using Newton's second law, which states that the net force on an object is equal to its mass times its acceleration. So, in this case, the tension at point P would be equal to the sum of the masses times the acceleration plus some clown magic. Just kidding again! No clown magic here, just some good ol' physics.
To find the tension in the string at point P, we need to analyze the forces acting on the blocks.
Let's consider the block with mass m first. The only force acting on it is the tension force T1 in the upper string. According to Newton's second law (F=ma), we have:
T1 - mg = ma ----- (Equation 1)
Next, let's consider the block with mass M. The forces acting on it are the tension force T2 in the lower string, the tension force T1 in the upper string (which is also acting on the block with mass m), and the gravitational force mg. According to Newton's second law:
mg - T1 - T2 = Ma ----- (Equation 2)
In this system, both blocks have the same downward acceleration a. So, we can substitute the value of a from Equation 1 into Equation 2:
mg - (T1 + T2) = Ma
From Equation 1, we can express T1 in terms of m, a, and g:
T1 = ma + mg
Substituting this into the equation above:
mg - (ma + mg + T2) = Ma
Simplifying, we get:
- T2 = Ma - ma
Rearranging the equation, we have:
T2 = ma - Ma ----- (Equation 3)
The tension at point P is the tension force T2 in the lower string. Therefore, the tension in the string at point P is given by Equation 3:
Tension at point P = T2 = ma - Ma