What is the mass of the hanging block in this system in equilibrium?

In summary, the question asks for the mass of the hanging block m2 that will keep the system in equilibrium. This can be determined by setting the tension in the rope equal to the weight of m2. The mass m1 on the incline has a known value, and the smooth inclined surface can be used to find the components of forces acting on the blocks. The equilibrium condition for m1 can then be written using the tension in the rope.
  • #1
jessicax07
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0

Homework Statement


T
here are 2 blocks connected by a string, as shown in the first image attached. The smooth inclined surface makes an angle of 40 degrees with the horizontal, and the block on the incline has a mass m1 = 7.9kg. What is the mass of the hanging block m2 that will cause the system to be in equilibrium.


Homework Equations



[tex]\sum[/tex]F = ma
then find the components...

The Attempt at a Solution



I know that I have to set up a free body diagram then break everything up into components. I also know that objects in equilibrium do not accelerate. But I can't figure out how to find the one mass. What equation would I use or what would I set things equal to?
 

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  • #2
Since the bodies are in equilibrium, they don't accelerate. Which means that the rope is keeping them still.
The tension in the rope is thus equal to the weight of m2. This is the equilibrium condition for m2.
Now try to right the condition up for m1. (i.e. the tension in the rope is equal to ...).
 

Related to What is the mass of the hanging block in this system in equilibrium?

1. What are Newton's Laws of Motion?

Newton's Laws of Motion are a set of three physical laws that describe the behavior of objects in motion. They were developed by Sir Isaac Newton in the 17th century and are the foundation of classical mechanics.

2. What is the first law of motion?

The first law of motion, also known as the law of inertia, states that an object at rest will remain at rest and an object in motion will remain in motion at a constant speed and in a straight line unless acted upon by an external force.

3. What is the second law of motion?

The second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be expressed mathematically as F = ma, where F is force, m is mass, and a is acceleration.

4. What is the third law of motion?

The third law of motion, also known as the law of action and reaction, states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another, the second object will exert an equal and opposite force back on the first object.

5. How do Newton's Laws of Motion apply to real-life situations?

Newton's Laws of Motion can be seen in everyday situations, such as when a car accelerates or decelerates, when a ball is thrown, or when a person walks. They are also crucial in understanding and predicting the motion of objects in more complex scenarios, such as space travel or sports. These laws are fundamental to our understanding of the physical world and are used in many fields, including engineering, physics, and astronomy.

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