/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 An inelastic ball is dropped fro... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 13

An inelastic ball is dropped from a height of \(100 \mathrm{~m}\). If \(20 \%\) of its energy is lost, to what height will the ball rise? (A) \(80 \mathrm{~m}\) (B) \(40 \mathrm{~m}\) (C) \(60 \mathrm{~m}\) (D) \(20 \mathrm{~m}\)

Short Answer

Expert verified
The ball will rise to a height of \(80 \mathrm{~m}\) after losing 20% of its energy. The correct answer is (A) \(80 \mathrm{~m}\).

Step by step solution

01

Calculate initial potential energy

The ball is dropped from a height of 100m, so its initial potential energy is: \(PE = mgh\) Where: - PE is the potential energy - m is the mass of the ball - g is the acceleration due to gravity (approximately \(9.81 \mathrm{m/s^2}\)) - h is the initial height (100m) Since we don't know the mass of the ball, we will leave it as m for now.
02

Calculate initial kinetic energy

Since the ball is dropped, its initial kinetic energy is 0.
03

Calculate total mechanical energy

The total mechanical energy of the ball is the sum of its potential and kinetic energy. In this case, the total mechanical energy is equal to its initial potential energy, which is: \(TME = PE = mgh\)
04

Calculate final mechanical energy

The problem states that the ball loses 20% of its energy when it hits the ground. Therefore, we need to find the final mechanical energy after losing 20% of its energy: \(Final~TME = 0.8 \times (Initial~TME)\) \(Final~TME = 0.8 \times (mgh)\)
05

Calculate final height

Now we need to find the height the ball will rise to after losing 20% of its energy. To do this, we will equate the final mechanical energy to the potential energy at the final height: \(mgh' = 0.8 \times (mgh)\) Where: - \(h'\) is the final height - Other symbols have the same meaning as before Notice that the mass of the ball (m) will cancel out: \(gh' = 0.8 \times (gh)\) Now, we can solve for the final height: \(h' = 0.8 \times h\) \(h' = 0.8 \times 100\) \(h' = 80\) The ball will rise to a height of 80m after losing 20% of its energy. The correct answer is (A) \(80 \mathrm{~m}\).

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