Find è and W in the figure below where w1 = 17.0 N, w2 = 31.0 N, and á = 67.5°, assuming that the arrangement is at rest.
To solve this problem, we need to understand the equilibrium conditions for an object at rest. In this case, we have a figure with two forces, W1 and W2, acting at angles of á and θ, respectively. The objective is to find the magnitudes of the forces W1 and W2.
The first step is to label all the forces and angles in the figure. In this case, we know that W1 has a magnitude of 17.0 N and W2 has a magnitude of 31.0 N. The angle á is given as 67.5°.
Next, we should draw a free-body diagram of the forces acting on the object. We can represent the forces W1 and W2 as vectors pointing in the direction of their respective forces, with their magnitudes labeled. We also need to include the unknown force è, which is acting in the y-direction.
Next, we can resolve the forces into their x and y components. We know that the force è only has a y-component since it is acting vertically. The x-component of è is zero since it is not acting horizontally.
To find the y-component of è, we can use the fact that the object is at rest, so the sum of all the forces in the y-direction must be zero. This gives us the equation:
W1sin(á) + W2sin(θ) + è = 0
Substituting in the given values, we have:
17.0sin(67.5°) + 31.0sin(θ) + è = 0
We can solve this equation to find the value of è.
Finally, we can find the magnitude of W by using the fact that the sum of all the forces in the x-direction must also be zero since the object is at rest. This gives us the equation:
W1cos(á) - W2cos(θ) = 0
Substituting in the given values, we have:
17.0cos(67.5°) - 31.0cos(θ) = 0
We can solve this equation to find the value of W.
To summarize:
1. Label all the forces and angles in the figure.
2. Draw a free-body diagram to visualize the forces acting on the object.
3. Resolve the forces into their x and y components.
4. Set up equations using the equilibrium conditions and the given values.
5. Solve the equations to find the unknown forces è and W.