Newtons Theory question - 911 - help exam tommorow

In summary, the conversation discusses the calculation of resultant force and acceleration of an object with two perpendicular ropes attached to it. The suggested method is vector summation by drawing each force vector and finding the magnitude of the resultant force. The final answer is 47 N and 1.2 m/s^2 for the force and acceleration, respectively.
  • #1
quarkboy
7
0
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.
 
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  • #2
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.
 
  • #3
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
:smile:
 
  • #4
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.
 
  • #5
Yes. Correct.

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

1. What is Newton's theory?

Newton's theory, also known as Newtonian mechanics, is a set of physical laws that describe the motion of objects in the universe. It states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force.

2. Who is Sir Isaac Newton and why is he important?

Sir Isaac Newton was an English physicist and mathematician who is widely recognized as one of the most influential scientists in history. He is best known for his law of gravitation and his three laws of motion, which laid the foundation for classical mechanics.

3. How does Newton's theory relate to 911?

Newton's theory does not directly relate to the events of 911. However, the principles of Newton's theory can be applied to analyze the physical forces and motion involved in the collapse of the World Trade Center towers.

4. Is Newton's theory still relevant today?

Yes, Newton's theory is still relevant and widely used in many fields of science and engineering. It is the basis for many modern technologies and has been extensively tested and confirmed through experiments and observations.

5. How can I apply Newton's theory to my daily life?

You can apply Newton's theory in many ways, such as understanding the forces involved in driving a car, throwing a ball, or even walking. It can also help you understand the behavior of objects in everyday situations and make predictions about their motion.

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