In the system shown in the figure, the pulley is smooth. The rope is massless and cannot be stretched. Determine the acceleration of system a and the tensions T1 and T2.
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00:00Hi friends, Wednesday always brings a smile to the second half of the week.
00:07The display on this screen shows several blocks connected by a rope through a pulley.
00:13Now, we are asked to calculate the tension in the rope.
00:20While thinking about the problem, let's watch this animation.
00:25This circle is a pulley.
00:28On the right and left sides there are several blocks.
00:34It seems that the block on the right side is heavier than the block on the left side.
00:39Automatically, the block on the right side will slide down.
00:44This condition is probably not written in the problem sheet that the pulley does not rotate while the rope passes through it.
00:51Because the pulley is slippery, we must understand conditions like this.
00:58Now let's examine the free body diagram of each body.
01:03This system consists of three bodies.
01:06Block 1, block 2, and block 3.
01:12Each block has a gravitational force directed toward the center of the earth.
01:18The taut string indicates tension in the string.
01:24This appears to be the only force acting on each body.
01:30Each block has a different resultant force depending on the force acting on it.
01:36For block 1, m1g minus t1 equals m1a.
01:42Although the direction of the force is negative toward the y-axis, we prefer to consider the direction parallel to the object's motion to be positive.
01:50This is the reference we use.
01:56For block 2, m2g plus t1 minus t2 equals m2a.
02:04For block 3, t2 minus m3g equals m3a.
02:11The values of several physical quantities can be found on the problem sheet.
02:18Up to this point, we need mathematical skills.
02:23Based on experience in solving problems, simply add all the equations to eliminate all tension in the rope.
02:3090 is equal to 15a.
02:34O is equal to 6 meters per second squared.
02:39This means the block on the right side will move downward with an acceleration of 6 meters per second squared.
02:48Now, we will calculate the tension in the rope.
02:52Choose the simplest equation.
02:55Using equation 1, 80 minus t1 is equal to 8 times 6.
03:02From here, t1 is equal to 32 newtons.
03:08Using equation 3, t2 minus 30 is equal to 3 times 6.
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