Vector Addition: Find the Resultant Vector

In summary: Show what you have tried and where you got stuck. That is the best way to learn.But since I have already solved this problem for you, here is the solution:Since you have chosen the x-axis parallel to the incline, you can use the geometry of the figure to find the components of P:Py = Psinθ = Psin15°Px = Pcosθ = Pcos15°Now, using the equations of equilibrium:ΣFy = 0 = Qy + Wy + PyΣFx = 0 = Qx + Wx + PxSubstituting the known values:Qy = Qsinθ = 600sin(-30°) = -300Wy =
  • #1
jove8414
5
0

Homework Statement


[/B]
The block shown in Fig. P-223 is acted upon by its weight W = 200lb, a horizontal force Q = 600lb and the pressure P exerted by the inclined plane. The resultant R of these forces is up and parallel to the incline thereby sliding the block up it. Determine P and R. Hint: Take one axis parallel to the incline. Ans: R = 293lb

https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xpf1/v/t1.0-9/q82/s720x720/11015301_1002403293112217_141332182178751666_n.jpg?oh=13938518c6c5618236be3f0fbd8ce4aa&oe=562F0B00&__gda__=1445053718_99ad9a3e011c3cbad300e49a737ea336

Homework Equations


[/B]R = SummationFx + SummationFy
Fx = Fcos0
Fy = Fsin0

The Attempt at a Solution


I don't know how to start the problem. In the worktext, this is the only problem that has unknown magnitude(P). To get the R I need first to P. The hint says take one axis parallel to the incline, I will be able to form an isosceles triangle with P as the leg but I still won't be able to solve for the magnitude of P... How do I start this problem?This problem is from Engineering Mechanics by Singer, it is our homework #213-223, I'm already done with the rest. The previous problems has all given magnitude and angle(some you need to solve for the angle, but still are easy except this one because of unknown value of P).
 
Last edited:
Physics news on Phys.org
  • #2
Uhh, there's no way to find the pressure P without knowing the area of the bottom of the box. Perhaps they meant to say that P is a force.

With that assumption, that P is a force, you can determine it's magnitude by the fact that the block is in equilibrium in the normal direction (it doesn't float away from the plane and it doesn't move inside the plane).
 
  • #3
jove8414 said:

Homework Statement


[/B]
The block shown in Fig. P-223 is acted upon by its weight W = 200lb, a horizontal force Q = 600lb and the pressure P exerted by the inclined plane. The resultant R of these forces is up and parallel to the incline thereby sliding the block up it. Determine P and R. Hint: Take one axis parallel to the incline. Ans: R = 293lb

https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xpf1/v/t1.0-9/q82/s720x720/11015301_1002403293112217_141332182178751666_n.jpg?oh=13938518c6c5618236be3f0fbd8ce4aa&oe=562F0B00&__gda__=1445053718_99ad9a3e011c3cbad300e49a737ea336

Homework Equations


[/B]R = SummationFx + SummationFy
Fx = Fcos0
Fy = Fsin0

The Attempt at a Solution


I don't know how to start the problem. In the worktext, this is the only problem that has unknown magnitude(P). To get the R I need first to P. The hint says take one axis parallel to the incline, I will be able to form an isosceles triangle with P as the leg but I still won't be able to solve for the magnitude of P... How do I start this problem?

This problem is from Engineering Mathematics by Singer, it is our homework #213-223, I'm already done with the rest. The previous problems has all given magnitude and angle(some you need to solve for the angle, but still are easy except this one because of unknown value of P).
The vector P may be unknown, although you do know its direction.

However, you do know something about the resultant R. If you follow the hint, then you know on of the components of R. Right ?
 
  • Like
Likes jove8414
  • #4
@sammy:

Great! I got it now thanks. What I did is I made the incline my x-axis (hint). With that I now have:

Q = 600∠-30
W = 200∠-120

and then:

Qx = 519.62
Qy = -300
Wx = -100
Wy = -173.21

and since R is parallel to the incline which is now the x-axis therefore ΣRy = 0 = Qy + Wy + Py or

Py = 473.21... using the given 15' angle, I get Px = -126.8

R = ΣRy + ΣRx
R = ΣRx
R = Qx + Wx + Px

R = 292.82


Sweet! Thanks a lot :)
 
  • #5
Can you show the solution on how did you get the value of Py and Px?
 
  • #6
pebtobias said:
Can you show the solution on how did you get the value of Py and Px?
You should post your own attempt first.
 

Related to Vector Addition: Find the Resultant Vector

What is vector addition?

Vector addition is the process of combining two or more vectors to find the resultant vector. It involves both magnitude and direction, and can be represented graphically or algebraically.

How do you find the resultant vector?

To find the resultant vector, you must first break down each vector into its horizontal and vertical components. Then, add the horizontal components together and the vertical components together. Finally, use the Pythagorean theorem to find the magnitude of the resultant vector and trigonometry to find its direction.

What is the difference between vector addition and scalar addition?

Vector addition involves adding both magnitude and direction, while scalar addition only involves adding magnitude. This means that vector addition takes into account the direction of the vectors, while scalar addition does not.

Can you add more than two vectors at once?

Yes, you can add as many vectors as you would like at once. The process is the same as adding two vectors, but you will have more components to add together and more trigonometric calculations to find the resultant vector's direction.

What is the purpose of finding the resultant vector?

The purpose of finding the resultant vector is to determine the overall displacement or velocity when multiple vectors are acting on an object. It allows us to combine the effects of each individual vector and understand the overall motion of the object.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
7K
  • Introductory Physics Homework Help
Replies
4
Views
14K
  • Introductory Physics Homework Help
Replies
9
Views
4K
  • Other Physics Topics
Replies
6
Views
1K
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
6
Views
5K
  • Introductory Physics Homework Help
Replies
4
Views
9K
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
5
Views
2K
Back
Top