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Chapter 4: Problem 451

A body of mass \(1 \mathrm{~kg}\) is thrown upwards with a velocity $20 \mathrm{~m} / \mathrm{s}\(. It momentarily comes to rest after a height \)18 \mathrm{~m}\(. How much energy is lost due to air friction. \)(\mathrm{g}=10 \mathrm{~m} / \mathrm{s} 2)$ (A) \(20 \mathrm{~J}\) (B) \(30 \mathrm{~J}\) (C) \(40 \mathrm{~J}\) (D) \(10 \mathrm{~J}\)

Short Answer

Expert verified
The energy lost due to air friction is \(20 \mathrm{~J}\), which corresponds to option (A).

Step by step solution

01

Calculate initial kinetic energy (KE)

We can calculate the initial kinetic energy of the body using the formula KE = \(\frac{1}{2}\)mv², where m is the mass of the body (1 kg) and v is its initial velocity (20 m/s). This will give us the initial kinetic energy in Joules (J). KE = \(\frac{1}{2}(1 \mathrm{~kg})(20 \mathrm{~m/s})^2\) = \(200 \mathrm{~J}\)
02

Calculate final potential energy (PE)

Now, we need to find the final potential energy of the body when it reaches the height of 18 m. We can do this using the formula PE = mgh, where m is the mass (1 kg), g is the gravitational acceleration (10 m/s²), and h is the height (18 m). PE = (1 \mathrm{~kg})(10 \mathrm{~m/s²})(18 \mathrm{~m}) = \(180 \mathrm{~J}\)
03

Calculate net energy at the highest point

When the body momentarily comes to rest, its final kinetic energy will be 0 J, as it has stopped completely. Therefore, the net energy at the highest point will be equal to the final potential energy. Net energy = PE = \(180 \mathrm{~J}\)
04

Determine the energy lost due to air friction

To find the energy lost due to air friction, we need to subtract the net energy at the highest point from the initial kinetic energy. Energy loss = Initial KE - Net Energy = \(200 \mathrm{~J} - 180 \mathrm{~J} = 20 \mathrm{~J}\) So, the energy lost due to air friction is \(20 \mathrm{~J}\), which corresponds to option (A).

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