Question

impulse problem a
assume the mass of the bottle is 0.500 kg and it falls off the table for 0.200 m before the bungee cord starts to stop it. as the bungee cord just starts to stop it, the bottle will be traveling down at 2.00 m/s. assuming it takes the bungee cord 0.500 seconds to bring the bottle to rest, calculate the force the bottle experiences during this time.
the formula is \\(\vec{f}\delta t = m(\vec{v}_f - \vec{v}_0)\\)

Explanation:

Step1: List given values

$m=0.500\ \text{kg}$, $\vec{v}_0=-2.00\ \text{m/s}$ (downward as negative), $\vec{v}_f=0\ \text{m/s}$, $\Delta t=0.500\ \text{s}$

Step2: Rearrange impulse formula for force

$$\vec{F} = \frac{m(\vec{v}_f - \vec{v}_0)}{\Delta t}$$

Step3: Substitute values into formula

$$\vec{F} = \frac{0.500\ \text{kg} \times (0 - (-2.00\ \text{m/s}))}{0.500\ \text{s}}$$

Step4: Calculate the result

$$\vec{F} = \frac{0.500 \times 2.00}{0.500}\ \text{N} = 2.00\ \text{N}$$
(Positive sign means upward force)

Answer:

The force the bottle experiences is $\boldsymbol{2.00\ \text{N}}$ upward.