Gravity Crunch Bell Ringer
Physics Warm-Up • Universal Gravitation
Gravity Crunch Bell Ringer
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Date
Period
Core Strategy
Separate Coefficients from Exponents
\( F_g = G \frac{m_1 m_2}{r^2} \) | \( G = 6.67 \times 10^{-11} \, \text{N}\cdot\text{m}^2/\text{kg}^2 \)
1 Coefficients
Group mantissas together:
\( C = \frac{6.67 \times a_1 \times a_2}{(a_r)^2} \)
2 Exponent Rules
Multiply = add; divide = subtract:
\( \text{Power} = [(-11) + p_1 + p_2] - [2 \cdot p_r] \)
3 Recombine & Adjust
Standard scientific notation:
\( F_g = C \times 10^{\text{Power}} \rightarrow A \times 10^n \)
1
Guided Task: Deep Space Asteroids
Step-by-Step Scaffolding
Two mining asteroids in orbit:
\( m_1 = 4.0 \times 10^{12} \, \text{kg} \) \( m_2 = 2.0 \times 10^{15} \, \text{kg} \) \( r = 2.0 \times 10^6 \, \text{m} \)
Part A: Calculate Coefficients Only
\( \text{Coeff} = \frac{6.67 \times 4.0 \times 2.0}{(2.0)^2} = \frac{6.67 \times 8.0}{4.0} = \)
Coefficient value: ______________
Part B: Track Powers of Ten (Add & Subtract)
Top: \( (-11) + 12 + 15 = \) _____
Bottom: \( 2 \times 6 = \) _____
Net Exponent (Top - Bottom): \( 10^{\underline{\hspace{1.5cm}}} \)
Final Answer (Combine & Adjust to Standard Scientific Notation):
\( F_g = \) ___________________ \( \text{N} \)
2
Independent Solve: Probe & Dwarf Planet
Apply the Strategy
A space probe passes a distant moon:
\( m_1 = 5.0 \times 10^3 \, \text{kg} \) \( m_2 = 8.0 \times 10^{21} \, \text{kg} \) \( r = 2.0 \times 10^7 \, \text{m} \)
Coefficients Setup & Work
Coeff: ______________
Powers of Ten Work (Exponents)
Power: \( 10^{\underline{\hspace{1.5cm}}} \)
Final Gravitational Force (Standard Form):
\( F_g = \) ___________________ \( \text{N} \)
Exponent Rule Check (Don't Get Trapped!)
When squaring distance in the denominator, why is \( (3.0 \times 10^5)^2 \) equal to \( 9.0 \times 10^{10} \) instead of \( 9.0 \times 10^7 \) or \( 9.0 \times 10^{25} \)?
Rule justification: __________________________________________________________________________________________
