Question

A 30 kg mass is 5 m above the ground. How much work does gravity do to pull it down?Does that 30kg mass in the previous question have any energy in it?If the 30kg mass falls, using kinematics, can you determine the speed of that mass just before it hits the ground?

Answer 1

`\begin{gathered} 1,470J \\ \text{Yes} \\ 9.9m\/s \end{gathered}`

Step-by-step explanation

Parameters given:

Mass, m = 30 kg

Distance above the ground, d = 5 m

To find the amount of work that gravity does on the mass, we have to find the product of its weight and the distance of the mass above the ground:

`W=F\cdot d`

where F represents weight (since it is a force)

The weight of the mass is:

`\begin{gathered} F=m\cdot g \\ F=30\cdot9.8 \\ F=294N \end{gathered}`

where g = acceleration due to gravity

Hence, the work done by gravity is:

`\begin{gathered} W=294\cdot5 \\ W=1,470J \end{gathered}`

At every point during the mass's fall to the ground, it possesses both potential and kinetic energy, although in varying quantities at different points.

Hence, yes, it has energy in it.

Just before the mass hits the ground, its final kinetic energy is equal to its initial potential energy.

To find the speed of the mass, we have to first find that potential energy.

Potential energy is given by:

`\begin{gathered} PE=m\cdot g\cdot d \\ PE=30\cdot9.8\cdot5 \\ PE=1,470N \end{gathered}`

That is equivalent to its kinetic energy just before it hits the ground.

Kinetic energy is given by:

`KE=(1)/(2)mv^2`

where v = speed

Now, we can solve for speed from the formula above:

`\begin{gathered} 1470=(1)/(2)\cdot30\cdot v^2 \\ (1470\cdot2)/(30)=v^2 \\ \Rightarrow v^2=98 \\ v=\sqrt[]{98} \\ v=9.9m\/s \end{gathered}`

That is the speed of the mass just before it hits the ground.