A toy dart gun generates a dart with 0.180 kg.m/s momentum and a velocity of 4.1 m/s. What is the mass of the dart in grams rounded to 2 significant figures?

1 Answer
Jan 27, 2017

The mass of the toy dart is "0.044 kg"0.044 kg rounded to two significant figures.

Explanation:

Momentum is mass in motion. Momentum depends on the mass of the object in motion and its velocity. Because velocity is a vector quantity, momentum is a vector quantity, even though a direction was not included in this question.

The equation for momentum is color(red)(rho=m*v)ρ=mv, where rhoρ, (pronounced "roe") is momentum, mm is mass, and vv is velocity.

Known
rho=0.180color(white)(.)"kg"*"m/s"ρ=0.180.kgm/s

v="4.1 m/s"v=4.1 m/s

Unknown
m=???m=???

Solution
Rearrange the equation for momentum to isolate mass. Substitute the known values into the equation.

color(red)(m=rho/v)m=ρv

m=(0.180"kg"*cancel"m/s")/("4.1 "cancel"m/s")="0.044 kg" rounded to two significant figures