Questions & Answers: "Work, Energy, and Power"

The work done by the person against gravity is equal to the potential energy gained by the block. The formula for potential energy is $PE = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the height. Given: Mass ($m$) = 2 kg Height ($h$) = 5 m Acceleration due to gravity ($g$) = $10 \ m/s^2$ Work done ($W$) = $PE = mgh = 2 \times 10 \times 5 = 100 \ J$. Therefore, the work done by the person against gravity is 100 J. Options A, B, and D are incorrect as they do not match the calculated work done.

According to the Law of Conservation of Energy, the potential energy (PE) at the highest point is converted entirely into kinetic energy (KE) at the lowest point, assuming no energy loss. Potential Energy at the highest point ($PE_{top}$) = $mgh$ Kinetic Energy at the lowest point ($KE_{bottom}$) = $\frac{1}{2}mv^2$ By Conservation of Energy: $PE_{top} = KE_{bottom}$ $mgh = \frac{1}{2}mv^2$ We can cancel 'm' from both sides: $gh = \frac{1}{2}v^2$ Rearranging for $v$: $v^2 = 2gh \implies v = \sqrt{2gh}$ Given: Height ($h$) = 0.2 m Acceleration due to gravity ($g$) = $10 \ m/s^2$ $v = \sqrt{2 \times 10 \times 0.2} = \sqrt{4} = 2 \ m/s$. Therefore, the speed of the pendulum bob at its lowest point is 2 m/s. Options A, C, and D are incorrect based on the conservation of energy principle and calculation.

Power is defined as the rate at which work is done or energy is transferred. First, calculate the work done by the pump to lift the water. The work done against gravity is equal to the potential energy gained by the water. Work done ($W$) = $mgh$ Given: Mass ($m$) = 500 kg Height ($h$) = 20 m Acceleration due to gravity ($g$) = $10 \ m/s^2$ $W = 500 \times 10 \times 20 = 100000 \ J$. Next, calculate the power using the formula: Power ($P$) = $\frac{Work \ done}{Time}$ Given: Time ($t$) = 10 s $P = \frac{100000 \ J}{10 \ s} = 10000 \ W$. Therefore, the power of the pump is 10000 W. Options A, B, and D are incorrect as they do not match the calculated power.