Simplifying a Confusing Force Problem: Understanding Acceleration and Magnitude

[maniacp08]

Here is a picture of the problem.

The question is:
A force F0 causes an acceleration of 17 m/s2 when it acts on an object of mass m sliding on a frictionless surface. Find the magnitude of the acceleration of the same object in the circumstances shown in each figure below.
Figure (a)
m/s2
Figure (b)
m/s2

My problem is I am not too sure what the problem wants me to do.

It gives me the acc. of 17 m/s^2 but how come it asks me to find the magnitude of the acc.?
Can someone please rephrase this into simpler terms? I want to do this on my own but I am just confuse on what this problem want me to do. Any help would be appreciated.

 

[Topher925]

It sounds to me like the problem just wants you to deal with vectors. Your right in that it is not a very well written problem. I believe the author is referring to a 17 m/s^2 acceleration if the force Fo is applied in a single direction.

For diagrams a and b the force Fo is acting in multiple directions and your job is to find the resulting acceleration due to Fo acting in those different directions.

 

[Doc Al]

It gives me the acc. of 17 m/s^2 but how come it asks me to find the magnitude of the acc.?

17 m/s^2 is the acceleration of the mass when only one force Fo acts by itself. (You'll need this fact later.) When multiple forces act, as shown in the diagrams, the net force and thus the acceleration will be different.

Hint: Find the net force in each diagram in terms of Fo.

 

[maniacp08]

So it accelerates an object 17m/s^2 when 1 Fo is applied.

Diagram 1 shows 2 Fo, 1 pushing horizontally and 1 vertically.
Im assume they are pushed simultaneously, so wouldn't the object move
at an angle of 45 degrees? or in the middle?
Would I need to find that magnitude?

So I would need to find the vertical and horizontal component, but the Force of Fo is not given nor the mass so, is it 17m/s^2, the components?

 

[Doc Al]

So it accelerates an object 17m/s^2 when 1 Fo is applied.

Right.

Diagram 1 shows 2 Fo, 1 pushing horizontally and 1 vertically.
Im assume they are pushed simultaneously, so wouldn't the object move
at an angle of 45 degrees? or in the middle?

Yes.

Would I need to find that magnitude?

Absolutely.

So I would need to find the vertical and horizontal component, but the Force of Fo is not given nor the mass so, is it 17m/s^2, the components?

Find the magnitude of the net force as a multiple of Fo. Then you'll be able to compare that force to the one that gives you a 17 m/s^2 acceleration.

 

[maniacp08]

Find the magnitude of the net force as a multiple of Fo. Then you'll be able to compare that force to the one that gives you a 17 m/s^2 acceleration.

Im not quite sure what I should do with so little info the problem gives me.

I have to find the "hypotenuse" in the triangle it forms with the angle 45 degrees.
I know the horizontal and vertical component is Fo.
Then I go blank on what to do next.

 

[Doc Al]

If the sides of the triangle were 10 units long, what would be the hypotenuse? Then answer the question if the sides were Fo units long.

 

[maniacp08]

I think I got it.

Is the first 1
root of(Fo^2 + Fo^2)
root of(2Fo^2)
square root(2) * F0
Then root(2) * 17 m/s^2

and the 2nd 1 is
square root(5) * F0

Is this correct?

 

[Redbelly98]

I think I got it.

Is the first 1
root of(Fo^2 + Fo^2)
root of(2Fo^2)
square root(2) * F0
Then root(2) * 17 m/s^2

Yes.

and the 2nd 1 is
square root(5) * F0

Not quite. The two vectors are not at right angles, so the Pythagorean Theorem does not apply.
Try using trig to express the forces in terms of x- and y-components.

 

[maniacp08]

I split it in half so each angle is 22.5

so is sin22.5x = F0

x = 17m/s^2 / sin22.5

Is this approach good?

 

[Doc Al]

I split it in half so each angle is 22.5

so is sin22.5x = F0

x = 17m/s^2 / sin22.5

Is this approach good?

No. The trick of going down the middle works when the forces are equal, as in the first example, but not when they are unequal. Instead, call the direction of the 2Fo force the x-direction. Now find the x and y components of both forces and then the resultant. Then you can use the Pythagorean theorem to find the magnitude of the net force.

 

[hejo]

I'm having difficulty with this same question (although my Fo has an acceleration of 16m/s^2). I understand how to find the magnitude of the acceleration for diagram a, but still don't understand how to go about breaking into components of x and y for diagram b. Can anyone explain further? Thanks!

 

[Doc Al]

Call the direction of the 2Fo force the x-direction. So, what's the x & y components of the 2Fo force? And the x & y components of the other force, which is at a 45 degree angle to the x-axis?

(This is just like finding the components of any other vector.)

 

[hejo]

Thanks Doc Al,

I just tried what you said and understood where I was going wrong. I wasn't separating the forces into 2 separate components, but rather tried solving with them together. After following your instructions, I got the answer right! Thanks for your help!