Balance the force to find the angle

In summary, the problem involves finding the total mass needed to balance the force F on a force table. A mass of 175 grams is placed on a hanger with a mass of 50 grams, giving a total mass of 225 grams. The hanger is attached to a pulley with low friction and hung at an angle of 120°. To balance the force F, another mass needs to be hung at an angle of -30° from the positive x-axis. Using the equations Tx=Tcos(theta), Ty=Tsin(theta), and T=mg, the total mass is calculated to be 225 grams and the angle is found to be -30° by drawing the negative of the angle and measuring from the positive x-axis
  • #1
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Homework Statement



A mass, m = 175 gram is placed on a hanger which has a mass of 50 g, giving a total mass of 225 g. The hanger is then hung at an angle of 120° over a pulley attached to the force table by using a string of negligible mass. The pulley over which the string rests has very low frictional force.
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In order to balance the force F another mass needs to be hung from the force table. What is the total mass (mass plus hanger) needed to balance the force F? At what angle should the mass be hung? Give your angle from the positive x-axis.

Homework Equations


Tx=Tcos(theta)
Ty=Tsin(theta)
A=SQRT(X^2+Y^2)
T= mg

The Attempt at a Solution


T = 2.2 N from .225*9.8
Tx=2.2cos120=-1.10N
Ty=2.2cos120=1.91N

Mass to balance = 225g
Angle = -30degrees?

the way I was told to find the angle was to draw the negative of the angle, so I drew the vector on the opposite side of the 2nd quadrant onto the 4th quadrant. Then find the angle according to the +x-axis. I drew the angle and for me I got -30 degrees since I assumed that since the 1st quadrant is 90degrees, then the remaining degree on the 2nd quadrant is obviously 30 and the opposite of it into the 4th quadrant would be -30?Any hints/help would be appreciated. Thanks
edit :Wow - nevermind... I figured this out lol. Ignoring this problem and coming back to it an hour later works wonders :P
 
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  • #2
Hey...how'd you figure it out? I'm stuck at the same place and with your previous answers lol. Any help would be appreciated
 

Related to Balance the force to find the angle

1. What does it mean to "balance the force"?

When we say "balance the force", we are referring to the concept of equilibrium, where the net force acting on an object is equal to zero. This means that the object is not accelerating and is either at rest or moving with a constant velocity.

2. Why is it important to balance the force?

Balancing the force is important because it allows us to accurately predict the motion of an object. When the forces acting on an object are unbalanced, the object will accelerate in the direction of the net force. By balancing the forces, we can determine the angle at which the object will move.

3. How do we find the angle when balancing the force?

To find the angle when balancing the force, we use the concept of vector addition. We break down the forces acting on the object into their horizontal and vertical components, and then use trigonometric functions to find the angle between the resultant force and the horizontal axis.

4. What factors affect the balance of the force?

The balance of the force is affected by the magnitude and direction of the individual forces acting on the object. It is also influenced by the mass and acceleration of the object itself. Additionally, external factors such as friction and air resistance can also affect the balance of the force.

5. How is balancing the force used in real-world applications?

Balancing the force is used in various real-world applications, such as designing structures, calculating trajectories in sports, and predicting the movement of objects in physics experiments. It is also essential in engineering and mechanics, as it allows us to understand and control the motion of machines and vehicles.

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