# 18.2 Conservation of energy  (Page 3/3)

 Page 3 / 3

## Potential energy

1. A tennis ball, of mass $120\phantom{\rule{2pt}{0ex}}\mathrm{g}$ , is dropped from a height of $5\phantom{\rule{2pt}{0ex}}\mathrm{m}$ . Ignore air friction.
1. What is the potential energy of the ball when it has fallen $3\phantom{\rule{2pt}{0ex}}\mathrm{m}$ ?
2. What is the velocity of the ball when it hits the ground?
2. A bullet, mass $50\phantom{\rule{2pt}{0ex}}\mathrm{g}$ , is shot vertically up in the air with a muzzle velocity of $200\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ . Use the Principle of Conservation of Mechanical Energy to determine the height that the bullet will reach. Ignore air friction.
3. A skier, mass $50\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ , is at the top of a $6,4\phantom{\rule{2pt}{0ex}}\mathrm{m}$ ski slope.
1. Determine the maximum velocity that she can reach when she skies to the bottom of the slope.
2. Do you think that she will reach this velocity? Why/Why not?
4. A pendulum bob of mass $1,5\phantom{\rule{2pt}{0ex}}\mathrm{kg}$ , swings from a height A to the bottom of its arc at B. The velocity of the bob at B is $4\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ . Calculate the height A from which the bob was released. Ignore the effects of air friction.
5. Prove that the velocity of an object, in free fall, in a closed system, is independent of its mass.

## Summary

• The potential energy of an object is the energy the object has due to his position above a reference point.
• The kinetic energy of an object is the energy the object has due to its motion.
• Mechanical energy of an object is the sum of the potential energy and kinetic energy of the object.
• The unit for energy is the joule (J).
• The Law of Conservation of Energy states that energy cannot be created or destroyed, but can only be changed from one form into another.
• The Law of Conservation of Mechanical Energy states that the total mechanical energy of an isolated system remains constant.
• The table below summarises the most important equations:
 Potential Energy ${E}_{P}=mgh$ Kinetic Energy ${E}_{K}=\frac{1}{2}m{v}^{2}$ Mechanical Energy ${E}_{M}={E}_{K}+{E}_{P}$

## End of chapter exercises: gravity and mechanical energy

1. Give one word/term for the following descriptions.
1. The force with which the Earth attracts a body.
2. The unit for energy.
3. The movement of a body in the Earth's gravitational field when no other forces act on it.
4. The sum of the potential and kinetic energy of a body.
5. The amount of matter an object is made up of.
2. Consider the situation where an apple falls from a tree. Indicate whether the following statements regarding this situation are TRUE or FALSE. Write only 'true' or 'false'. If the statement is false, write down the correct statement.
1. The potential energy of the apple is a maximum when the apple lands on the ground.
2. The kinetic energy remains constant throughout the motion.
3. To calculate the potential energy of the apple we need the mass of the apple and the height of the tree.
4. The mechanical energy is a maximum only at the beginning of the motion.
5. The apple falls at an acceleration of $9,8\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-2}$ .
3. A man fires a rock out of a slingshot directly upward. The rock has an initial velocity of $15\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ .
1. What is the maximum height that the rock will reach?
2. Draw graphs to show how the potential energy, kinetic energy and mechanical energy of the rock changes as it moves to its highest point.
4. A metal ball of mass $200\phantom{\rule{2pt}{0ex}}\mathrm{g}$ is tied to a light string to make a pendulum. The ball is pulled to the side to a height (A), $10\phantom{\rule{2pt}{0ex}}\mathrm{cm}$ above the lowest point of the swing (B). Air friction and the mass of the string can be ignored. The ball is let go to swing freely.
1. Calculate the potential energy of the ball at point A.
2. Calculate the kinetic energy of the ball at point B.
3. What is the maximum velocity that the ball will reach during its motion?
5. A truck of mass $1,2\phantom{\rule{2pt}{0ex}}\mathrm{tons}$ is parked at the top of a hill, $150\phantom{\rule{2pt}{0ex}}\mathrm{m}$ high. The truck driver lets the truck run freely down the hill to the bottom.
1. What is the maximum velocity that the truck can achieve at the bottom of the hill?
2. Will the truck achieve this velocity? Why/why not?
6. A stone is dropped from a window, $6\phantom{\rule{2pt}{0ex}}\mathrm{m}$ above the ground. The mass of the stone is $25\phantom{\rule{2pt}{0ex}}\mathrm{g}$ . Use the Principle of Conservation of Energy to determine the speed with which the stone strikes the ground.

explain and give four Example hyperbolic function
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Abdullahi
hi mam
Mark
find the value of 2x=32
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
use the y -intercept and slope to sketch the graph of the equation y=6x
how do we prove the quadratic formular
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
The fundamental frequency of a sonometer wire streached by a load of relative density 's'are n¹ and n² when the load is in air and completly immersed in water respectively then the lation n²/na is
Properties of longitudinal waves