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Potential energy

  1. A tennis ball, of mass 120 g , is dropped from a height of 5 m . Ignore air friction.
    1. What is the potential energy of the ball when it has fallen 3 m ?
    2. What is the velocity of the ball when it hits the ground?
  2. A bullet, mass 50 g , is shot vertically up in the air with a muzzle velocity of 200 m · 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 kg , is at the top of a 6,4 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 kg , swings from a height A to the bottom of its arc at B. The velocity of the bob at B is 4 m · 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 = m g h
Kinetic Energy E K = 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 m · s - 2 .
  3. A man fires a rock out of a slingshot directly upward. The rock has an initial velocity of 15 m · 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 g is tied to a light string to make a pendulum. The ball is pulled to the side to a height (A), 10 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 tons is parked at the top of a hill, 150 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 m above the ground. The mass of the stone is 25 g . Use the Principle of Conservation of Energy to determine the speed with which the stone strikes the ground.

Questions & Answers

marginal cost formula
Nandu Reply
you should differentiate the total cost function in order to get marginal cost function then you can get marginal cost from it
boniphace
formula of cross elasticity of demand
Theresia Reply
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Priyanka Reply
what is ceteris parabus
Priyanka
Ceteris paribus - Literally, "other things being equal"; usually used in economics to indicate that all variables except the ones specified are assumed not to change.
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owusu
it's a summary of opportunity cost depicted on a curve.
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igwe Reply
disaster management cycle
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Fedric Wilson Taylor also define management as the act of knowing what to do and seeing that it is done in the best and cheapest way
OLANIYI
difference between microeconomics and macroeconomic
Ugyen Reply
microeconomics is the study of individual units, firm and government while macroeconomics is the study of the economic aggregates.
okhiria
The classical theory of full employment
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the situation that prevails when economic forces balance so that economic variables neither increase nor decrease
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salihu Reply
Economics is important because it helps people understand how a variety of factors work with and against each other to control how resources such as labor and capital get used, and how inflation, supply, demand, interest rates and other factors determine how much you pay for goods and services.
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Properties of longitudinal waves
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Source:  OpenStax, Siyavula textbooks: grade 10 physical science [caps]. OpenStax CNX. Sep 30, 2011 Download for free at http://cnx.org/content/col11305/1.7
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