Newtons Theory question - 911 - help exam tommorow

[quarkboy]

Newtons Theory & Vector Solution

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Q.

Two ropes are attached to a 40kg object.

The 1st rope applies a force of 25N & 2nd rope applies force of 40N.

If the ropes are perpendicular to each other, what is the resultant acceleration of the object ?

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A.

A bit confused, drew diagram. But could not figure out what method of calculation to do.

Thanks in advance.

 

[StephenPrivitera]

This is a simple exercise in vector summation. Draw each force vector. Place the tail of the second on the head of the first. They should be perpendicular. Now draw a vector from the tail of the first to the head of the second. This last vector is called the resultant vector. This is how all vectors summate. Find the magnitude of the resultant force the same way you would find the resultant displacement and then apply Newton's laws to find the acceleration.

 

[quarkboy]

this is what I worked out... CORRECT ANSWER!

1. calculated R = resultant vector = 47 N Force using trigonometry.
2. F = ma , Therefore a = F/m
3. acceleration is 1.2 m/s-2

There could be another way to work this problem out, not sure. Thanks for the solution StephenP

 

[HallsofIvy]

The way I would do this is set up a coordinate system so that the first force (25 N)is acting along the x-axis and the second (40 N) is acting along the y axis. That means that the two force vectors have components (25, 0) and (0, 40). Their sum is, of course, (25,40).
The "length" of that vector (the scalar force) is √(25²+ 40²)= 47 Newtons, as you got.

 

[quarkboy]

Yes. Correct.

I do believe that was the goal of the question, to do it via your method. Thank you for your enlightened thinking.