## Mastering Physics Solutions: Understanding Newton’s Laws

Understanding Newton’s Laws

Part A = The net force acting on it is zero.
Part B = The net force applied to the block is zero.
Part C = It could be moving to the left, moving to the right, or be instantaneously at rest.
Part D = Moving with a constant nonzero acceleration.
Part E = Cannot have a magnitude equal to 5 N.

Solutions Below:

Part A

An object cannot remain at rest unless which of the following holds?

1. The net force acting on it is zero
2. The net force acting on it is constant and nonzero
3. There are no forces at all acting on it
4. There is only one force acting on it

1 is correct. If all forces cancel out, the object can remain at rest.

Part B

If a block is moving to the left at a constant velocity, what can one conclude?

1. There is exactly one force applied to the block.
2. The net force applied to the block is directed to the left.
3. The net force applied to the block is zero.
4. There must be no forces at all applied to the block.

Although this may seem counter intuitive, remember the physics definition of force: F = ma. Since the velocity is constant, acceleration must be zero, and therefore force must also be zero.

Part C

A block of mass 2 kg is acted upon by two forces: 3 N (directed to the left) and 4 N (directed to the right). What can you say about the block’s motion?

1. It must be moving to the left.
2. It must be moving to the right.
3. It must be at rest.
4. It could be moving to the left, moving to the right, or be instantaneously at rest.

This question is a perfect example of why Mastering Physics can be so misleading. Although it may seem like the problem is giving you all of the relevant information, the correct answer requires you to speculate. If the block were already moving, the addition of the two forces wouldn’t necessarily move it in either direction or cause it to stop. For example, if the block were moving left at 100km/h, obviously a force of just 3 N isn’t going to send it to the left. So the correct answer is #4. Just remember that the acceleration of an object doesn’t tell you anything about its velocity (the speed and direction at which it is moving).

Part D

A massive block is being pulled along a horizontal frictionless surface by a constant horizontal force. The block must be __________.

1. Continuously changing direction
2. Moving at constant velocity
3. Moving with a constant nonzero acceleration
4. Moving with continuously increasing acceleration

Remember that F = ma. If there is a force, there must be acceleration. Since the force is constant, the acceleration must also be constant, therefore #3 is the correct answer.

Part E

Two forces, of magnitude 4 N and 10 N, are applied to an object. The relative direction of the forces is unknown. The net force acting on the object __________.
Check all that apply.

1. Cannot have a magnitude equal to 5 N
2. Cannot have a magnitude equal to 10 N
3. Cannot have the same direction as the force with magnitude 10 N
4. Must have a magnitude greater than 10 N

Since force is a vector quantity you can deduce the smallest possible force using different forces from exactly opposite directions. E.g. subtracting 4 from 10. The result is 6, therefore you know 6 is the smallest net force possible and #1 must be a correct answer.

#2 cannot be correct because it’s possible to add 2 vectors with magnitudes 4 and 6 where the resulting vector has a magnitude of 10. For example, 6 N directly to the right (x direction at zero degrees) plus 4 N at 33.7 °. That would give a triangle with hypotenuse 10 and sides 4 and 6.

#3 can’t be correct because we’ve already seen how the force could be as small as 6 N.

Finally, #4 can’t be correct because obviously both forces can be applied in the same direction, which would mean the resulting net force is also in the same direction. So #1 is the only correct answer.

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