Question

calculate the potential gravitational energy for the lamp and its speed if it falls. the potential gravitational energy= 2 j 1.9 j 19 j the speed if it falls= 10 m/s² 6 m/s² 19 m/s²

Explanation:

Step1: Calculate potential - gravitational energy

Use the formula $U = mgh$, where $m = 1\ kg$, $g= 9.8\ m/s^{2}$, and $h = 2\ m$.
$U=1\times9.8\times2= 19.6\ J\approx19\ J$

Step2: Calculate the speed when it falls

By conservation of mechanical energy, the potential - energy at the initial height is converted into kinetic energy at the bottom. The formula for kinetic energy is $K=\frac{1}{2}mv^{2}$. Since $K = U$ (neglecting air - resistance), we have $\frac{1}{2}mv^{2}=U$.
We know $U = 19.6\ J$ and $m = 1\ kg$. Then $\frac{1}{2}\times1\times v^{2}=19.6$, so $v^{2}=2\times19.6 = 39.2$, and $v=\sqrt{39.2}\approx 6\ m/s$.

Answer:

The potential gravitational energy = 19 J
The speed if it falls = 6 m/s