# Physics Homework Problem Newtons Laws of Motion

• destro47
In summary, you need to use the cosine rule to find the magnitude of the resultant force and use the sine rule to find the angle at which the resultant force acts.
destro47
I have this problem on a web assignment due on the 20th of this month. A few of the problems have completely blown my mind including the following:

A force F0 causes an acceleration of 18 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

I know F=ma, but doesn't seem to be enough to solve this problem. I have also included a picture of the diagram which accompanied this problem. I would appreciate any help or guidance that could point me in the right direction.

You need to resolve the two forces into a single force.

Do this by drawing a diagram in which the two forces form two sides of a triangle. The third side represents the resultant force.

Since you know two of the side lengths, and also the angle which separates them, it is possible to calculate the magnitude of the third force using the cosine rule.
$$c^{2} = a^{2} + b^{2} - 2abCosC$$

It is also possible to determine the angle that the resultant force acts at by using the sine rule.
a/SinA = b/SinB = c/SinC

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If I think that I understand you correctly ur saying to use the law of cosines to find the magnitude of the resultant force graphically. That makes sense, but what I don't understand is how that would work. Only the acceleration is given, the magnitude of the force is not given in this problem. Also, the mass of the box is not given so how would the law of cosines be applicable here?

never mind...makes sense now. I feel like a total retard. I used Pythagorean theorum to solve part A. I just realized that the pythagorean theorum is becomes a special case of the law of cosines when angle C = 90*

Well for the first case you have all you need, you should be able to intuitively "see" the resultant force. Now take the component of each applied force in that direction, using this and the known force $$F_0$$ you can solve for the unknown acceleration.

Once you have the acceleration you can solve for mass m and use it in part b.Edit: I'm to slow. Glad you got it.

## 1. What are Newton's Laws of Motion?

Newton's Laws of Motion are three fundamental laws developed by Sir Isaac Newton to explain the behavior of objects in motion. They are:

1. The law of inertia: An object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity unless acted upon by an external force.
2. The law of acceleration: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be represented by the equation F=ma.
3. The law of action and reaction: For every action, there is an equal and opposite reaction.

## 2. How do I apply Newton's Laws of Motion to solve physics homework problems?

To apply Newton's Laws of Motion, you must first identify the forces acting on the object and their directions. Then, use the appropriate equation(s) to solve for the unknown variable. It is important to draw a free-body diagram and label all the forces to help visualize the problem.

## 3. What is the difference between mass and weight in Newton's Laws of Motion?

Mass is the measure of the amount of matter in an object, while weight is the measure of the force of gravity acting on an object. In Newton's Laws of Motion, mass is used to calculate the acceleration of an object, while weight is used to calculate the force of gravity acting on the object.

## 4. Can Newton's Laws of Motion be applied to objects at rest?

Yes, the first law of motion (law of inertia) can be applied to objects at rest. It states that an object at rest will remain at rest unless acted upon by an external force. In other words, if there is no net force acting on an object, it will remain at rest.

## 5. How do I calculate the net force on an object using Newton's Laws of Motion?

To calculate the net force on an object, you must first identify all the forces acting on the object and their directions. Then, use the equation F=ma to calculate the net force. If the net force is zero, the object will remain at rest or continue moving at a constant velocity. If the net force is not zero, the object will accelerate in the direction of the net force.

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