Inclined Plane System with 3 blocks

[golgiapparatus88]

A little note: I've been using the Course Saver lectures and they're wonderful. One of the best things I learned was how to solve these pulley problems and inclined plane problems fast. (i can explain if necessary)

This question is in the Kaplan High Yield book. Sorry if this is confusing, here's the question:

Blocks 1 and 2 are held together by a rope on an inclined plane of 30 degrees. The third block is tied to another rope (connected to block 2) and is hanging off the inclined plane. (m1 = 15, m2 = 10, m3 = 30). What are the tensions between block 1 and 2, and the tension between block 2 and 3.

I was able to solve for the first question and get 120N which is the correct answer. Unfortunately, I tried to solve the second tension and my answer was incorrect. The correct 2nd tension is 200.5N


If this question is way to long for an MCAT test (which i'm sure it is) can someone tell me the take-home message of the test? It's obvious the tensions between the masses will be different. Is there a way to tell which will have the larger tension and which will be smaller? Thanks!!

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[ilovemcat]

First thing you must figure out is if this system of objects is accelerating.

You have the two mass system and the single mass system hanging in opposite directions.

The two mass system has a downward force of magnitude:

Fleft = (m1+m2)gsin(theta)
Fleft = (15+10)(10)(1/2)
Fleft = 125 N

The single mass system has a magnitude of:
Fright = (m1)g
Fright = 30(10)
Fright = 300 N

Solving for the NET Force, we get:
Fnet = Fright - Fleft
Fnet = 300N - 125N
Fnet = 175N

Similar to a Pulley System, we can find the acceleration of the whole system:

(55)a = 175N
a ~ 3 m/s^2

Plugging in this acceleration value to find the tension between mass 1 and 2:

(m1)a = T - m1gsin(theta)
(15)(3) = T - 15(10)(1/2)
45 + 75 = T
120 N = T

Similarly, we can solve for the second tension between mass 2 and 3 in the same way.

(m1+m2)a = T - m1gsin(theta) - m2gsin(theta)
25a = T - 75N - 50 N
25(3) = T - 125N
200 N = T

 

[ilovemcat]

By the way, I wouldn't eliminate the idea of having a problem like this on the MCAT. It's very easy for them to ask this same question but award multiple points for different answers (ie. acceleration of system or tensions 1 and 2).

You should realize the Tension between m2 and m3 will be larger than the tension between m1 and m2 simply because it's pulling against more weight. However, the system as a whole accelerates at the same rate.

 

[golgiapparatus88]

Thanks guys! I understand now. And yea, I think this is definitely a good type of MCAT problem. Just like a pendulum with 2 masses at the end...which actually, I should probably review as well