QUARTER FINAL STAGE 2024
Accra Academy: 45 points
Oyoko Methodist SHS: 36 points
St. Joseph Seminary SHS: 28 points
ROUND 4 - TRUE OR FALSE
FIRST SET OF QUESTIONS
PREAMBLE
The angle between two concurrent forces of equal magnitude is increased from $0$ degrees to $180$ degrees.
1. The magnitude of the resultant of the two forces is greatest when the angle between them is 0 degrees.
ANSWER: TRUE
EXPLANATION:
When the angle is $0^\circ$, the two forces act in the exact same direction.
The magnitude of their resultant is simply the algebraic sum of their individual magnitudes ($R = F + F = 2F$), which is the maximum possible value.
2. The magnitude of the resultant of the two forces is minimum when the angle between them is $90$ degrees.
ANSWER: FALSE
EXPLANATION:
The magnitude of the resultant decreases continuously as the angle increases from $0^\circ$ to $180^\circ$.
The absolute minimum occurs when the angle is $180^\circ$, where the forces point in opposite directions and completely cancel each other out ($R = F - F = 0$).
3. The angle between the resultant of the two forces and any of them is 60 degrees when the angle between the forces is 120 degrees
ANSWER: TRUE
EXPLANATION:
Since the two concurrent forces are equal in magnitude, their resultant vector perfectly bisects the angle between them.
Half of $120^\circ$ is exactly $60^\circ$.
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PRACTICE QUESTIONS
PREAMBLE 1
Two forces of 3.0 N and 4.0 N act at a point, and the angle between them can be changed.
1. The greatest resultant is 7.0 N.
ANSWER: TRUE
EXPLANATION:
The forces act in the same direction: $3.0 + 4.0$.
2. The resultant is 5.0 N when the forces are perpendicular.
ANSWER: TRUE
EXPLANATION:
$\sqrt{3.0^2 + 4.0^2} = 5.0$.
3. The resultant can be 0.50 N.
ANSWER: FALSE
EXPLANATION:
The smallest possible resultant is $4.0 - 3.0 = 1.0$ N.
PREAMBLE 2
Two equal forces F act at a point with an angle of 120° between them.
1. The resultant has magnitude F.
ANSWER: TRUE
EXPLANATION:
$R^2 = F^2 + F^2 + 2F^2\cos120^\circ = F^2$.
2. The resultant makes 60° with each force.
ANSWER: TRUE
EXPLANATION:
For equal forces the resultant bisects the angle.
3. The resultant is zero.
ANSWER: FALSE
EXPLANATION:
It is zero only when the angle is 180°.
PREAMBLE 3
Two equal forces F act at a point at right angles.
1. The resultant has magnitude $F\sqrt{2}$.
ANSWER: TRUE
EXPLANATION:
$\sqrt{F^2 + F^2}$.
2. The resultant makes 45° with each force.
ANSWER: TRUE
EXPLANATION:
It bisects the right angle.
3. The resultant has magnitude 2F.
ANSWER: FALSE
EXPLANATION:
2F is the resultant when the forces act together in one direction.