1. Conservation of Energy

Taking the value of $\displaystyle g$ to be $\displaystyle 9.8 ms^{-2}$.

Body of mass $\displaystyle 5kg$ falls freely from rest a distance of $\displaystyle 3m$, find the kinetic energy acquired by this body.
Let the height above the ground be $\displaystyle h$.

Initially $\displaystyle KE = 0$, and Gravitational Energy (PE) = $\displaystyle mgh = 5gh$.

Due to the conservation of energy, we know that this total of energy stays the same. So at our point 3 metres below the starting point:

$\displaystyle KE = 2.5v^2$, $\displaystyle PE = 5g(h-3)$.

Not sure how to work out the KE acquired by the body, and have I written the equations right?

Part 2: If the particle is brought to rest by a force of $\displaystyle 70N$, find the further distance fallen.
No idea where to start on this one, any help would be greatly appreciated.

2. Body of mass 5kg falls freely from rest a distance of 3m, find the kinetic energy acquired by this body.

$\displaystyle \Delta KE = -\Delta GPE$

$\displaystyle \Delta KE = -(mgh_f - mgh_0) = -mg(\Delta h) = -mg(-3) = 3mg$

go ahead and find the velocity ... you'll need it for part 2.

Part 2: If the particle is brought to rest by a force of 70N, find the further distance fallen.

$\displaystyle F_{net} = ma$

$\displaystyle 70 - mg = ma$

$\displaystyle a = \frac{70 - 5g}{5}$

$\displaystyle v_f = 0$

now use the equation $\displaystyle v_f^2 = v_0^2 + 2a(\Delta y)$ to determine $\displaystyle \Delta y$ ... remember that $\displaystyle \Delta y < 0$

3. Originally Posted by skeeter
Body of mass 5kg falls freely from rest a distance of 3m, find the kinetic energy acquired by this body.

$\displaystyle \Delta KE = -\Delta GPE$

$\displaystyle \Delta KE = -(mgh_f - mgh_0) = -mg(\Delta h) = -mg(-3) = 3mg$

go ahead and find the velocity ... you'll need it for part 2.

For the velocity, $\displaystyle \frac{1}{2}mv^2 = 3mg.$, so $\displaystyle v = \sqrt{6g} \approx 7.668$

Just to clarify, $\displaystyle h_f$ is the initial height?

Originally Posted by skeeter
Part 2: If the particle is brought to rest by a force of 70N, find the further distance fallen.

$\displaystyle F_{net} = ma$

$\displaystyle 70 - mg = ma$

$\displaystyle a = \frac{70 - 5g}{5}$

$\displaystyle v_f = 0$

now use the equation $\displaystyle v_f^2 = v_0^2 + 2a(\Delta y)$ to determine $\displaystyle \Delta y$ ... remember that $\displaystyle \Delta y < 0$
So from your equation, $\displaystyle v_f^2 = v_0^2 + 2a(\Delta y)$.

So $\displaystyle 6g + 2(14 - g)(\Delta y) = 0$

$\displaystyle \Delta y = \frac{-6g}{2(14 - g)} = \frac{-3g}{14 - g} = -7$

So the further distance fallen is 7 metres?

4. Originally Posted by craig

For the velocity, $\displaystyle \frac{1}{2}mv^2 = 3mg.$, so $\displaystyle v = \sqrt{6g} \approx 7.668$

Just to clarify, $\displaystyle h_f$ is the initial height?

no, $\displaystyle \textcolor{red}{h_f}$ is final height

So from your equation, $\displaystyle v_f^2 = v_0^2 + 2a(\Delta y)$.

So $\displaystyle 6g + 2(14 - g)(\Delta y) = 0$

$\displaystyle \Delta y = \frac{-6g}{2(14 - g)} = \frac{-3g}{14 - g} = -7$

So the further distance fallen is 7 metres?

correct
...

5. Thanks again.