Trouble finding direction of two force vectors

[Gradyjenkinz]

Homework Statement

[/B]
A block of mass 2kg is accelerated by the two forces F1 = 8i + 3j and F2 = -5i - 7j, (a) What is the net force on the block in unit vector notation, and what is its magnitude and direction? (b) What is the magnitude and direction of the acceleration?

Homework Equations

I'm not sure of the equation for the direction.

The Attempt at a Solution

I was able to dot the two vectors to get the Force, but I am stuck from here.

 

[JeremyG]

By convention, i,j,k are the unit vectors (of length 1) in the positive x,y and z axis respectively. By using i,j,k you have already taken into account for direction.

 

[Gradyjenkinz]

By convention, i,j,k are the unit vectors (of length 1) in the positive x,y and z axis respectively. By using i,j,k you have already taken into account for direction.

In the back of my book it gives answers, and the answer for this involves a degree though.

 

[JeremyG]

Yes, that is the answer for the second part of the question, part (a):

and what is its magnitude and direction?

I must've misunderstood your question.

You already have the net force in vector notation, am i right? Noting that i and j are unit vectors in the x and y direction, resolve your net force vector into the x and y direction. Then you should be able to see what you need to do to get the direction.

Hint: you need trigonometry

 

[gneill]

Homework Statement

[/B]
A block of mass 2kg is accelerated by the two forces F1 = 8i + 3j and F2 = -5i - 7j, (a) What is the net force on the block in unit vector notation, and what is its magnitude and direction? (b) What is the magnitude and direction of the acceleration?

Homework Equations

I'm not sure of the equation for the direction.

The Attempt at a Solution

I was able to dot the two vectors to get the Force, but I am stuck from here.

Can you show your work so far? Note that forces sum to yield a net force.

 

[Gradyjenkinz]

Can you show your work so far? Note that forces sum to yield a net force.

Yeah sure. So far I dotted the two vectors and I got Fnet = 3i - 4j, then F=5 for the magnitude. I then plotted the vectors on a graph and not sure what to do from here.

 

[SteamKing]

Yeah sure. So far I dotted the two vectors and I got Fnet = 3i - 4j, then F=5 for the magnitude. I then plotted the vectors on a graph and not sure what to do from here.

I don't know what you did here, but the dot product of two vectors is a scalar, not another vector.

https://www.mathsisfun.com/algebra/vectors-dot-product.html

The resultant of two vectors F₁ and F₂ is found by vector addition, or F_res = F₁ + F₂

In other words, you add the i and j components of each vector together to produce the resultant vector.

 

[JeremyG]

Yeah sure. So far I dotted the two vectors and I got Fnet = 3i - 4j, then F=5 for the magnitude. I then plotted the vectors on a graph and not sure what to do from here.

Plot your net force similarly. Do you understand how and why the magnitude of 3i - 4j is 5?

 

[Mister T]

Yeah sure. So far I dotted the two vectors and I got Fnet = 3i - 4j,

Note that what you did was not a dot product, it's a sum. You would write (8i + 3j)+(-5i - 7j) = 3i - 4j, not (8i + 3j)⋅(-5i - 7j) = 3i - 4j.

To find the angle, make a drawing of 3i - 4j.

 

[Gradyjenkinz]

Plot your net force similarly. Do you understand how and why the magnitude of 3i - 4j is 5?

Thank you, I got it. I plotted it and then took the inverse tan to get the angle.