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Chapter 3: Problem 10

An object moving at a constant velocity is acted on by several forces. Which of the following is true? i. All the forces are acting in the same or opposite directions. ii. The vector sum of the forces must be zero. iii. The magnitude of the forces must be the same. (A) i (B) ii (C) iii (D) i and iii (E) i, ii and iii

Short Answer

Expert verified
(A) All forces act in the same or opposite direction (B) The vector sum of the forces is zero (C) The magnitudes of the forces are the same. Answer: (B) The vector sum of the forces is zero.

Step by step solution

01

Newton's 1st Law of Motion

According to Newton's 1st Law of Motion, an object will remain at rest or continue moving at a constant velocity if there are no net external forces acting on it (or if the net force acting on it is zero). In the given exercise, the object has a constant velocity. Therefore, the net force on the object must be zero.
02

Analyzing Statement i

The first statement says that all forces are acting in the same or opposite directions. It is not necessary for all forces to be in the same or opposite direction to satisfy Newton's 1st Law. The forces could be acting in different directions, and their vector sum could still be zero. Hence, statement i is not necessarily true.
03

Analyzing Statement ii

The second statement says that the vector sum of the forces must be zero. As mentioned in Step 1, for an object to have a constant velocity, the net force acting on it must be zero. This means that the sum of all forces (in terms of vectors) should be zero. Hence, statement ii is true.
04

Analyzing Statement iii

The third statement says that the magnitude of the forces must be the same. This statement is not necessarily true, as different forces can have different magnitudes but still result in a net force of zero when combined. Thus, statement iii is not necessarily true.
05

Choosing the correct answer

Based on our analysis of the statements, only statement ii is true. Therefore, the correct answer is (B) ii.

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