Pulleys / Newton's Laws

In summary: Since T2 acts down, it should be -T2, and W2 acts down, so it should be -W2. You'll figure it out. In summary, the student is attempting to solve a problem involving Atwood's machine with two blocks connected by a cord. They have drawn free-body diagrams for each block and correctly identified the forces acting on them as tension and weight. However, they have made an error in their equations by not accounting for the direction of the forces. By correcting this error, they will be able to find the correct tension in the cord.
  • #1
martyk
4
0

Homework Statement


The figure shows two blocks connected by a cord (of negligible mass) that passes over a frictionless pulley (also of negligible mass). The arrangement is known as Atwood's machine. Block 1 has mass m1 = 0.900 kg; block 2 has mass m2 = 2.70 kg. What is the tension in the cord? Assume a y-axis has its positive direction upward.

http://img5.imageshack.us/img5/50/q55u.jpg [Broken]


Homework Equations


F = ma


The Attempt at a Solution



Ok can someone tell me what is wrong with my approach here. I drew two free-body diagrams, and both basically the same. My free body diagrams have only 2 forces acting on the boxes. Upwards is the tension, and downwards is the weight of the boxes. So let T1 and W1 be the forces on the first box, and T2 and W2 be the forces on the second box. And based on this scenario, I know that T1 and T2 are equal, so is acceleration

I summed up the forces acting on the first box, which leaves T1 - W1 = ma1, since the problem is asking for tension of the cord, I rearranged the equation to this T1 = ma1 + W1. I did the exact same with the second box. T2 - W2 = ma2, hence T2 = ma2 + W2. Since T1 = T2, I set these two equations equal to find A (note that a1 and a2 should be equal also). After plugging in the numbers in the parameters I got acceleration as -9.8m/s. Plugged it back to the tension equation.
 
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  • #2
martyk said:

Homework Statement


The figure shows two blocks connected by a cord (of negligible mass) that passes over a frictionless pulley (also of negligible mass). The arrangement is known as Atwood's machine. Block 1 has mass m1 = 0.900 kg; block 2 has mass m2 = 2.70 kg. What is the tension in the cord? Assume a y-axis has its positive direction upward.

http://img5.imageshack.us/img5/50/q55u.jpg [Broken]


Homework Equations


F = ma


The Attempt at a Solution



Ok can someone tell me what is wrong with my approach here. I drew two free-body diagrams, and both basically the same. My free body diagrams have only 2 forces acting on the boxes. Upwards is the tension, and downwards is the weight of the boxes. So let T1 and W1 be the forces on the first box, and T2 and W2 be the forces on the second box. And based on this scenario, I know that T1 and T2 are equal
very good so far
, so is acceleration
their magnitudes are equal, but what about their directions?
I summed up the forces acting on the first box, which leaves T1 - W1 = ma1, since the problem is asking for tension of the cord, I rearranged the equation to this T1 = ma1 + W1.
good
I did the exact same with the second box. T2 - W2 = ma2, hence T2 = ma2 + W2.
Here's your error. It's all in the plus or minus sign.
 
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  • #3
T = 0.900(-9.8) + 2.7(-9.8) which gave me T = -24.57N. What did I do wrong?

Your approach is correct, but there are a few errors in your calculations. First, the acceleration should be positive, not negative, since the blocks are accelerating upwards. So your equation for T should be T = ma1 + W1 = ma2 + W2. Secondly, you have mixed up the masses in your calculation for T. The equation should be T = m1a1 + m2a2. Plugging in the values, we get T = (0.900)(9.8) + (2.70)(9.8) = 29.16 N. This is the tension in the cord.
 

1. What is a pulley?

A pulley is a simple machine that consists of a wheel with a groove around its circumference and a rope or chain running over the wheel. It is used to lift or move objects by changing the direction of the force applied.

2. How does a pulley work?

A pulley works by distributing the weight of an object over multiple ropes or chains. This reduces the amount of force needed to lift the object. The pulley also changes the direction of the force, making it easier to lift the object vertically.

3. What are the three types of pulleys?

The three types of pulleys are fixed, movable, and compound. A fixed pulley is attached to a stationary object and only changes the direction of the force. A movable pulley is attached to the object being lifted and moves with it. A compound pulley combines the features of both fixed and movable pulleys to provide even more mechanical advantage.

4. How do pulleys relate to Newton's Laws of Motion?

Pulleys demonstrate Newton's First Law of Motion, which states that an object at rest will remain at rest or an object in motion will remain in motion unless acted upon by an unbalanced force. In the case of a pulley, the weight of the object being lifted is the unbalanced force that causes the motion.

5. What are some real-life examples of pulleys?

Pulleys are commonly used in many everyday objects and machines, such as elevators, cranes, flagpoles, and even exercise equipment. They are also used in some medical devices, like traction systems, to help move and lift patients. In the home, pulleys can be found in window blinds, garage doors, and even some types of curtains.

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