Problem Solving Strategies Question
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Grade 10 Problem Solving Strategies CCSS: HSN-Q.A.1
Rob is writing a physics test. For one of the problems, he needs the gravitational force formula for the force of gravity between two objects. He's not sure he remembers it correctly. He believes it is
[math]F_g = (G \ m_1 \ m_2)/r[/math],
where [math]F_g[/math] is the force, measured in Newtons; [math]G[/math] is the gravitational constant, measured in [math]"N"*"m"^2//"kg"^2[/math]; [math]m_1, m_2[/math] are the masses of the two objects measured in kilograms; and [math]r[/math] is the distance between the objects, measured in meters. Using dimensional analysis, is his formula correct? Why or why not?
[math]F_g = (G \ m_1 \ m_2)/r[/math],
where [math]F_g[/math] is the force, measured in Newtons; [math]G[/math] is the gravitational constant, measured in [math]"N"*"m"^2//"kg"^2[/math]; [math]m_1, m_2[/math] are the masses of the two objects measured in kilograms; and [math]r[/math] is the distance between the objects, measured in meters. Using dimensional analysis, is his formula correct? Why or why not?
- Yes, since [math]("N" * "m")/("kg"^2) xx "kg"/1 xx "kg"/1 xx 1/("m") = "N"[/math].
- No, since [math]("N" * "m"^2)/("kg"^2) xx "kg"/1 xx "kg"/1 xx 1/("m") = "N"*"m"[/math].
- No, since [math]("N" * "m"^2)/("kg"^2) xx 1/"kg" xx 1/"kg" xx "m"/1 = ("N" * "m"^3)/ ("kg"^4)[/math].
- No, since [math]("N" * "m"^2)/("kg"^2) xx "kg"/1 xx "kg"/1 xx "m"/1 = "N" * "m"^3[/math].
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