a 2.80 kg mass is dropped from a height of 4.50 m. what is the kinetic energy of the mass when it is 1.50 m…

Explanation:

Step1: Calculate initial potential energy

The formula for gravitational - potential energy is $U = mgh$. The initial height $h_1=4.50\ m$, mass $m = 2.80\ kg$ and $g = 9.8\ m/s^{2}$. So, $U_1=mgh_1=2.80\times9.8\times4.50$. $U_1 = 2.80\times9.8\times4.50=123.48\ J$.

Step2: Calculate potential energy at the given height

The height $h_2 = 1.50\ m$. Using the formula $U = mgh$, we get $U_2=mgh_2=2.80\times9.8\times1.50$. $U_2=2.80\times9.8\times1.50 = 41.16\ J$.

Step3: Use conservation of mechanical energy

In the absence of non - conservative forces (assuming no air resistance), the mechanical energy $E$ is conserved, $E = K+U$. Initially, the mass is at rest, so $K_1 = 0$ and $E = U_1$. At height $h_2$, $E=K_2 + U_2$. Since $E$ is conserved, $K_2=U_1 - U_2$. $K_2=123.48 - 41.16=82.32\ J$.

Answer:

$82.32$