# How do you find the force needed to accelerate a 0.007 kg pellet from rest to 125 m/s over a distance of 0.8 m along the barrel?

Mar 24, 2018

The force is $= 68.36 N$

#### Explanation:

Apply the equation of motion

${v}^{2} = {u}^{2} + 2 a s$

The initial velocity is $u = 0 m {s}^{-} 1$

The final velocity is $v = 125 m {s}^{-} 1$

The distance is $s = 0.8 m$

The acceleration is

$a = \frac{{v}^{2} - {u}^{2}}{2 s} = \frac{{125}^{2}}{2 \cdot 0.8} = 9765.625 m {s}^{-} 2$

The mass of the pellet is $= 0.007 k g$

According to Newton's Second Law of Motion

$F = m a$

The force is $F = 0.007 \cdot 9765.625 = 68.36 N$

Mar 24, 2018

$F = 68.36 N$

#### Explanation:

$m = 0.007$ $K g$
$u = 0$ $m {s}^{-} 1$
$v = 125$ $m {s}^{-} 1$
$s = 0.8 m$

Applying a motion equation:

${v}^{2} = {u}^{2} + 2 a s$
$15 625 = 1.6 a$
$a = 9765.625$ $m {s}^{-} 2$

Applying Newton's second law:

$F = m a$
$F = 0.007 \cdot 9765.625$
$F = 68.36 N$

Again, that's valid assuming we have no other forces on the motion axis acted on the object whatsoever.