X and Y - components of a force

In summary, the problem asks to calculate the x- and y- components of force C exerted by member BC on member ACD in a dual pulley setup. The sum of moment in the system and the sum of force in the x and y directions must equal zero in equilibrium. By determining the tension in the second cable, which is the ratio of the radii, and using the known forces and moments, the equations can be solved to find the components of force C.
  • #1
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Homework Statement


Calculate the x- and y- components of the force C which member BC exerts on
member ACD. The cables are wrapped securely around the two pulleys, which are
fastened together.
(Note the different diameters of the pulleys)
Problem


Homework Equations



The sum of moment in the systems = 0
The sum of force in Fx and Fy direction in an equilibrium condition equals zero.

Ok what I did was I differentiated each component and tried to calculate, but it didn't work. IN the attached file the question is shown.

Please Please I beg you all for help I have wasted a whole three days on it and even today I have slept for only 4 hours. Please it is due tommorow please help me.
 

Attachments

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  • #2


I'm assuming the duel pully set up pivots around point D. So your 100 kg mass creates a force downwards and a torque (moment) around D at a distance (radius) of 0.5 m which is resisted ONLY by the second cable with a radius of .25 m. From that information alone, you can determine the tension in the second cable since it's simply the ratio of the radius.

Now you have the tension in the second cable (from wall to pully) which creates a force in the X direction (horizontal) and a force down from the 100 kg weight in the Y direction (verticle). You also have two forces created by the beams at 45 degree to the wall. The sum of all the forces in the Y is the weight down and the verticle component of each beam at the wall. Similarly, the sum of all forces in the X direction is the second cable force and the horizontal component of each beam at the wall.

You also know that for each of the beams (ex: BC) there are no moments at the pinned locations so the force is directed along the axis of the beam (ex: so for BC, the X component of the force is equal to the Y component).

Write down the two equations (sum Fx and sum Fy) and solve.
 
  • #3


As a scientist, it is important to approach problems with a systematic and logical method. In this case, the first step would be to clearly define the variables and components involved in the problem. In this case, we have three members - BC, ACD, and the pulleys, and two components of force - X and Y.

The homework statement asks for the x- and y- components of the force C which member BC exerts on member ACD. To determine these components, we need to consider the forces acting on each member and apply the equations of equilibrium.

First, let's consider the forces acting on member BC. We have the force C acting on the member, as well as the tension forces in the cables wrapping around the pulleys. These tension forces can be broken down into their x- and y- components, which will also act on member BC. We can then use the equations of equilibrium to find the x- and y- components of force C on BC.

Next, let's consider the forces acting on member ACD. We have the force C acting on this member as well, along with the tension forces in the cables wrapping around the pulleys. Again, these tension forces can be broken down into their x- and y- components, which will also act on member ACD. Again, we can use the equations of equilibrium to find the x- and y- components of force C on ACD.

Once we have determined the x- and y- components of force C on both members, we can use the principle of transmissibility to find the x- and y- components of the force C exerted by member BC on member ACD.

In summary, to solve this problem, we need to clearly define the variables and components involved, consider the forces acting on each member, break down the tension forces into their x- and y- components, and use the equations of equilibrium to find the components of force C on both members. I hope this helps guide you in the right direction.
 

1. What are X and Y components of a force?

The X and Y components of a force refer to the horizontal and vertical parts of a force vector, respectively. They are used to break down a force vector into its individual parts in order to better understand its effects on an object.

2. How are X and Y components of a force calculated?

The X and Y components of a force can be calculated using trigonometric functions, specifically sine and cosine. The magnitude of the X component can be found by multiplying the magnitude of the force by the cosine of the angle between the force vector and the horizontal axis. The magnitude of the Y component can be found by multiplying the magnitude of the force by the sine of the angle between the force vector and the horizontal axis.

3. Why are X and Y components of a force important?

The X and Y components of a force are important because they allow us to analyze and understand the effects of a force on an object in a more detailed manner. By breaking down a force into its components, we can determine the direction and magnitude of the force acting on an object in each direction, which can be useful in various applications such as engineering and physics.

4. Can X and Y components of a force be negative?

Yes, X and Y components of a force can be negative. This occurs when the force vector is pointing in the opposite direction of the positive axis. The negative sign indicates that the force is acting in the negative direction, while a positive sign indicates that the force is acting in the positive direction.

5. How do X and Y components of a force affect an object?

The X and Y components of a force determine the overall motion of an object. The X component affects the horizontal motion of an object, while the Y component affects the vertical motion. These components work together to determine the overall direction and magnitude of the force acting on an object, which can result in various types of motion such as linear, circular, or projectile motion.

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