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?

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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?

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Answer 1 · 2017-01-27T01:30:41

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 $ρ = m \cdot v$ $color(red)(rho=m*v)$ , where $ρ$ $rho$ , (pronounced "roe") is momentum, $m$ $m$ is mass, and $v$ $v$ is velocity.

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

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

Unknown
$m = ? ? ?$ $m=???$

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

$m = \frac{ρ}{v}$ $color(red)(m=rho/v)$

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

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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

Explanation:

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