Question

A bullet of mass 0.02kg traveling at a speed of 100 m/s comes to rest when it has gone 0.4m into sand. Find the resisting force exerted by the sand.

Answer 1

`250\; {\rm N}`, assuming that the sand exerts a constant force.

Step-by-step explanation:

If the sand exerts a constant force, acceleration (deceleration) would be constant. Let
`a` denote this acceleration.

It is given that:

• displacement is
  `x = 0.4\; {\rm m}`.
• initial velocity is
  `u = 100\; {\rm m\cdot s^(-1)}`.

Additionally, final velocity is
`v = 0\; {\rm m\cdot s^(-1)}` when the object is at rest.

Rearrange the SUVAT equation
`v^(2) - u^(2) = 2\, a\, x` to find acceleration
`a`:

`\begin{aligned}a &= (v^(2) - u^(2))/(2\, x) \\ &= \frac{{(0\; {\rm m\cdot s^(-1)})}^(2) - {(100\; {\rm m\cdot s^(-1)})}^(2)}{2\, (0.4\; {\rm m})} \\ &= (-12500)\; {\rm m\cdot s^(-2)}\end{aligned}`.

Multiply acceleration by mass to find the net force:

`\begin{aligned}(\text{net force}) &= m\, a \\ &= (0.02\; {\rm kg})\, (-12500\; {\rm m\cdot s^(-2)}) \\ &= (-250)\; {\rm {N}}\end{aligned}`.

(Negative since velocity is decreasing.)

Assuming that all other forces are negligible. The force that the sand exerted would be equal to the net force,
`(-250)\; {\rm N}` (negative since this force opposes the motion.)