Question

question 5 of 10
you hold a metal block of mass 40 kg above your head at a height of 2 m. how much work is done by gravity if you let the block fall to the ground?
a. 80 j
b. -784 j
c. -80 j
d. 784 j

Explanation:

Step1: Identify the formula for work done by gravity

The work - done formula is $W = Fd\cos\theta$, where $F$ is the force, $d$ is the displacement, and $\theta$ is the angle between the force and the displacement. The force of gravity is $F = mg$ (where $m$ is the mass and $g$ is the acceleration due to gravity, $g= 9.8\ m/s^{2}$), the displacement $d = h$ (height), and for an object falling under gravity, $\theta = 0^{\circ}$ and $\cos\theta=\cos0^{\circ}=1$. So $W = mgh$.

Step2: Substitute the given values

Given $m = 40\ kg$, $h = 2\ m$, and $g = 9.8\ m/s^{2}$. Then $W=40\times9.8\times2$.
$W = 784\ J$. The work done by gravity is positive because the force of gravity and the displacement of the block are in the same direction.

Answer:

D. 784 J