Find Angles for Weight of 605 N

In summary, to find the angles θ1 and θ2, you can use the equations sinθ=opp/hyp and cosθ=adj/hyp, along with the fact that sin^2θ + cos^2θ = 1. To solve for these angles, you will need to break the forces on the hanging weight into horizontal and vertical components and set them equal to 0, then use F = ma to find the forces provided by the cables. From there, you can use trigonometry to find the values of θ1 and θ2 in degrees.
  • #1
jj8890
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[SOLVED] Force problem, need help

Homework Statement


Consider the 605 N weight held by two cables. The left-hand cable had tension 450 N and makes an angle of θ2 with the ceiling. The right-hand cable had tension 470 N and makes an angle of θ1 with the ceiling.
What are the angles θ1 and θ2 which are the angles of the right and left hand cables make with respect to the ceiling? Answer in units of degrees.



Homework Equations


sinθ=opp/hyp
cosθ=adj/hyp
sin^2θ + cos^2θ = 1


The Attempt at a Solution



I really do not know where to start here. I would appreciate any help. I am thinking that this has to do with using the above equations to find the angles but I am unsure how to use the 605 weight.
 
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  • #2
Before you break out the trigonometry, you should draw a diagram. Then, describe the motion (or lack of motion in this case) with some equations. Since this is a force problem, use F = ma. In these types of problems, break the forces on the weight into horizontal and vertical forces. Because the weight is motionless, the horizontal forces must sum to 0 and the vertical forces must sum to 0. What are providing the horizontal forces, and what are providing the vertical forces? How large are they?

Once you have your equations, you will find you have the sine or cosine of your angles θ1 and θ2 when you broke the forces from the cables into horizontal and vertical components. The rest is just solving for your angles.
 
  • #3
Ok, I understand that I would need to break the forces on the weight into horizontal and vertical but how exactly would you do that for the 450 N for example?
 
  • #4
After you draw your diagram, draw a perpendicular line connecting the hanging weight to the ceiling from which the cables hang. This will break the triangle formed by your cables and the ceiling into two right triangles, from which you can use trigonometry to find the horizontal and vertical forces.
 

Related to Find Angles for Weight of 605 N

1. How do I find the angles for a weight of 605 N?

To find the angles for a weight of 605 N, you will need to use the formula W = mg, where W is the weight in newtons, m is the mass in kilograms, and g is the acceleration due to gravity (9.8 m/s^2). Rearrange the formula to find the angle: tanθ = W/mg. Then, use a calculator to find the inverse tangent (arctan) of the resulting value to find the angle.

2. What is the weight of an object with an angle of 45 degrees?

The weight of an object with an angle of 45 degrees depends on the mass of the object. Using the formula W = mg, where g is 9.8 m/s^2, you can find the weight in newtons by multiplying the mass (in kilograms) by 9.8. For example, if the mass of the object is 10 kg, the weight would be 98 N at a 45 degree angle.

3. Can I use trigonometry to find the angles for any weight?

Yes, you can use trigonometry to find the angles for any weight as long as you have the mass and acceleration due to gravity for the object. Simply rearrange the formula tanθ = W/mg to find the angle.

4. How does the angle affect the weight of an object?

The angle does not directly affect the weight of an object. The weight is determined by the mass of the object and the acceleration due to gravity. However, the angle can affect the force acting on the object, which is equal to the weight. For example, if an object is on an incline, the weight will be divided into two components: one parallel to the incline and one perpendicular to the incline.

5. Can I use a protractor to measure the angle for a weight of 605 N?

No, you cannot use a protractor to measure the angle for a weight of 605 N. The weight is a measure of force, not an angle. You can use a protractor to measure the angle of an incline or ramp, but you will need to use trigonometry to find the angle for a specific weight.

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