A box has a mass of 20 kg, and a building has a height of 15 meters.
A) Find the force of gravity acting on the box.
B) Find the work required to lift the box from the ground to the roof of the building.
C) Find the potential energy of the box when it is on the roof of the building.
D) If the box is dropped off the roof of the building, find the kinetic energy and velocity of the box when it hits the ground.
A) Force =(20 \mathrm{~kg})\left(9.81 \frac{\mathrm{m}}{\mathrm{sec}^{2}}\right)=\mathbf{1 9 6 . 2} ~\mathbf{N}
B) Work = Force × Distance
Work =(196.2 \mathrm{~N})(15 \mathrm{~m})=\bf 2943 \mathbf{Nm}=\bf 2943 \mathbf{~J}
C) Potential Energy = Mass × Height × Gravity
Potential Energy =(20 \mathrm{~kg})(15 \mathrm{~m})\left(9.81 \frac{\mathrm{m}}{\mathrm{sec}^{2}}\right)=\bf 2943~ \mathbf{Nm}=\bf 2943 \mathbf{~J}
D) We know that Energy is conserved, so if the box is dropped from a height of 15 meters, its Kinetic Energy at Height = 0 meters will be the same as its potential energy at Height = 15 meters.
Kinetic Energy = 2943 Nm
To find the object’s velocity as it hits the ground:
Kinetic Energy =\left(\frac{1}{2}\right) Mass × Velocity²
\begin{aligned}& 2943 \,\mathrm{Nm}=\left(\frac{1}{2}\right)(20 \mathrm{~kg}) \times \mathrm{V}^{2}\\&\left(294.3 \frac{\mathrm{Nm}}{\mathrm{kg}}\right)\left(\frac{\frac{\mathrm{kg} \,\mathrm{m}}{\mathrm{sec}^{2}}}{1 \mathrm{~N}}\right)=294.3\left(\frac{\mathrm{m}^{2}}{\mathrm{sec}^{2}}\right)=\mathrm{V}^{2}\\& \rm V=\bf 17.16 \frac{\mathbf{m}}{\bf sec }\end{aligned}