PRELIMINARY STAGE 2024
Contest 4
Tsito SHTS: 55 points (Winner)
Methodist Girls’ SHS, Mamfe: 48 points
Notre Dame Seminary SHS: 45 points
Contest 5
Tema Methodist SHS: 54 points (Winner)
Shama SHS: 37 points
Bolgatanga SHS: 28 points
Contest 6
Wallahs Academy: 32 points (Winner)
O’Reilly SHS: 29 points
Adanwomase SHS: 25 points
ROUND 2 - SPEED RACE
QUESTION
If the spring constant of an unstretched spring is 640N per meter.
What extension of the spring does 1.6N produce.
ANSWER: $2.5 \times 10^{-3} \text{ m}$ (or $2.5 \text{ mm}$)
FORMULA
$x = \dfrac{F}{k}$
SOLUTION:
$x = \dfrac{1.6}{640}$
$x = \dfrac{16}{6400}$
$x = \dfrac{1}{400}$
$x = 0.0025 \text{ m}$
$x = 2.5 \times 10^{-3} \text{ m}$
Convert to millimeters:
$x = 0.0025 \times 1000$
$x = 25\times10^{-4} \times 1000$
$x = 2.5 \text{ mm}$
ANSWER: $2.5 \times 10^{-3} \text{ m}$ (or $2.5 \text{ mm}$)
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PRACTICE QUESTIONS
1. QUESTION: The spring constant of a spring is 480 N/m. What extension of the spring does a 1.2 N force produce?
ANSWER: 2.5 mm
SOLUTION:
$F = kx$
$x = \dfrac{F}{k}$
$x = \dfrac{1.2}{480}$
$x = \dfrac{12\times10^{-1}}{480}$
$x = \dfrac{1}{40} \times10^{-1}$
$x = 0.0025\text{ m}$
$x = 2.5\text{ mm}$
2. QUESTION: The spring constant of a spring is 320 N/m. What extension of the spring does a 2.4 N force produce?
ANSWER: 7.5 mm
SOLUTION:
$F = kx$
$x = \dfrac{F}{k}$
$x = \dfrac{2.4}{320}$
$x = \dfrac{24\times10^{-1}}{320}$
$x = \dfrac{3}{40} \times10^{-1}$
$x = 0.0075\text{ m}$
$x = 7.5\text{ mm}$
3. QUESTION: The spring constant of a spring is 250 N/m. What extension of the spring does a 1.5 N force produce?
ANSWER: 6.0 mm
SOLUTION:
$F = kx$
$x = \dfrac{F}{k}$
$x = \dfrac{1.5}{250}$
$x = \dfrac{15\times10^{-1}}{250}$
$x = \dfrac{3}{50} \times10^{-1}$
$x = 0.0060\text{ m}$
$x = 6.0\text{ mm}$
4. QUESTION: The spring constant of a spring is 640 N/m. What extension of the spring does a 3.2 N force produce?
ANSWER: 5.0 mm
SOLUTION:
$F = kx$
$x = \dfrac{F}{k}$
$x = \dfrac{3.2}{640}$
$x = \dfrac{32\times10^{-1}}{640}$
$x = \dfrac{1}{20} \times10^{-1}$
$x = 0.0050\text{ m}$
$x = 5.0\text{ mm}$
5. QUESTION: The spring constant of a spring is 250 N/m. What extension of the spring does a 0.75 N force produce?
ANSWER: 3.0 mm
SOLUTION:
$F = kx$
$x = \dfrac{F}{k}$
$x = \dfrac{0.75}{250}$
$x = \dfrac{75\times10^{-2}}{250}$
$x = \dfrac{3}{10} \times10^{-2}$
$x = 0.0030\text{ m}$
$x = 3.0\text{ mm}$
6. QUESTION: The spring constant of a spring is 360 N/m. What extension of the spring does a 0.90 N force produce?
ANSWER: 2.5 mm
SOLUTION:
$F = kx$
$x = \dfrac{F}{k}$
$x = \dfrac{0.90}{360}$
$x = \dfrac{9\times10^{-1}}{360}$
$x = \dfrac{1}{40} \times10^{-1}$
$x = 0.0025\text{ m}$
$x = 2.5\text{ mm}$
7. QUESTION: The spring constant of a spring is 560 N/m. What extension of the spring does a 1.4 N force produce?
ANSWER: 2.5 mm
SOLUTION:
$F = kx$
$x = \dfrac{F}{k}$
$x = \dfrac{1.4}{560}$
$x = \dfrac{14\times10^{-1}}{560}$
$x = \dfrac{1}{40} \times10^{-1}$
$x = 0.0025\text{ m}$
$x = 2.5\text{ mm}$
8. QUESTION: The spring constant of a spring is 480 N/m. What extension of the spring does a 3.6 N force produce?
ANSWER: 7.5 mm
SOLUTION:
$F = kx$
$x = \dfrac{F}{k}$
$x = \dfrac{3.6}{480}$
$x = \dfrac{36\times10^{-1}}{480}$
$x = \dfrac{3}{40} \times10^{-1}$
$x = 0.0075\text{ m}$
$x = 7.5\text{ mm}$
9. QUESTION: The spring constant of a spring is 320 N/m. What extension of the spring does a 1.6 N force produce?
ANSWER: 5.0 mm
SOLUTION:
$F = kx$
$x = \dfrac{F}{k}$
$x = \dfrac{1.6}{320}$
$x = \dfrac{16\times10^{-1}}{320}$
$x = \dfrac{1}{20} \times10^{-1}$
$x = 0.0050\text{ m}$
$x = 5.0\text{ mm}$