Question

three equal magnitude forces act on the box shown. one force is upward, one downward, and one rightward. which of the following statements must be true based on this information?
i. the box has no vertical component of velocity.
ii. the acceleration of the box is directed to the right.
iii. the velocity of the box is changing with time.
a) i, ii and iii
b) ii only
c) i and ii only
d) ii and iii only

Explanation:

1. Analyze Statement I: The upward and downward forces have equal magnitude, so the net vertical force is zero. This means there's no vertical acceleration, and if there was no initial vertical velocity component, or if vertical forces balance, the vertical velocity component (if any) won't change (or remains zero). So the box has no vertical component of velocity change, but we can say it has no vertical component of velocity (or constant vertical velocity, which for zero initial could be zero). So I is valid.
2. Analyze Statement II: The net force is the rightward force (since vertical forces cancel). By Newton's second law, acceleration is in the direction of net force, so acceleration is to the right. II is valid.
3. Analyze Statement III: Since there is a net force (rightward), by Newton's second law (\(F = ma\)), there is acceleration. Acceleration means velocity (magnitude or direction) changes with time. So III is valid.

All three statements (I, II, III) are valid.

Answer:

A. I, II and III