Kinetic Energy: energy of motion
Early physicists found that when matter interacts with matter, as in a collision between two objects, certain quantities are the same before the interaction as after the interaction. One of these is the total momentum of all the objects. Another quantity that is sometimes "conserved" like this is the total kinetic energy of all the objects involved.
The kinetic energy of an object is KE = ½ mv2 . The units are joules, and it is a scalar quantity.
Kinetic energy is energy of motion; the faster an object of mass m moves, the greater its kinetic energy. It turns out that when a hard, solid object hits another, the sum of kinetic energies is constant before and after the collision. When a soft object is involved, or if there is friction, or air resistance, or water resistance, kinetic energy is lost. It took a long time, and a lot of arguing and careful experimentation, for scientists to realize that the kinetic energy can change into other types of energy.
1. A baseball has a mass of 1.2 kg . What is its kinetic energy if it is tossed at 4.0 m/s ?
2.a. What is the KE of a 1-kg object moving at 1 m/s ?
b. What is the KE of the same 1-kg object moving at 2 m/s ? Is the KE doubled?
c. What is the KE of the same 1-kg object moving at 3 m/s ? Is the KE tripled?
3.a. What is the KE of a 1-kg bird flying at 2 m/s ?
b. What is the KE of the same 1-kg bird flying at 4 m/s ? Is the KE doubled?
c. What is the KE of the same 1-kg bird flying at 6 m/s ? Is the KE tripled?
4. What is the kinetic energy of a stationary 400 kg ostrich?
5. What is the mass of a rock that is rolling along at 10.0 m/s, with a kinetic energy of 310 J ?
6. Find the kinetic energy of a proton moving at 2.0 m/s (look in the Ref. Tbls. for mp.)
7. a. Look at your results for #2 and 3. When the speed is doubled, by what factor is the KE multiplied?
b. When the speed is tripled, the KE will be multiplied by a factor of ______.
- What is the speed of a 2.0 kg rabbit whose KE is 5.0 joules?
Work, a transfer of energy
"Work" is a physical quantity that has a very specific meaning. Work is only done when some force actually pushes an object over some distance. In order for work to be done, there must be a force, and something must move.
1. In which of these situations is work done? (neglect air resistance and assume frictionless wheels)
a) A bicycle is pedaled up a hill.
b) A bicycle coasts on a flat road.
c) A person pushes a desk across the room.
d) A person pushes against the wall.
e) A weight lifter holds a 3000 N weight over his head.
f) A little girl lifts a flower to her nose.
The greater the force, the greater the amount of work done. Also, the greater the distance the object is pushed, the greater the work done. Put together, we have a new equation: W = F x d, or just W = Fd. We say this as "work equals force times distance." The SI units of work are joules (J).
2. Calculate the amount of work done in each case:
a) A woman lifts a 12 newton weight up 2 meters. (Note that a "12 newton weight" means the force of gravity is 12 N, downward.)
b) A man pushes a cart along for 30 meters, with a force of 5 newtons.
c) A baseball bat is in contact with a baseball for 0.1 second, for a distance of 0.8 m, exerting a force of 300 N.
d) A 10 kg rock is lifted 1 meter. (You must first calculate the weight of the rock.)
The force that does the work is the force that acts in the direction of the object’s motion.
3. A 40 newton block is pushed 3 meters horizontally by a 12 newton force. How much work was done on the block?
You probably realized that one joule is the same as one newton times one meter, which we can call a "newton-meter". (1 J = 1 N∙m). Remember that one newton is equivalent to 1 kg.m/s2, so in terms of fundamental SI units, 1 J = 1 kg∙m2/s2
4. What is the SI unit for work?
5. Express your answer to #3 in terms of fundamental SI units (meters, kilograms, & seconds).
"Work" has the same units as energy. In fact, sometimes work is called "useful energy", because the energy is actually doing something, in making something move.
The amount of work done by something, when doing work on some other thing, is the amount of energy expended, and thus transferred. Some of that energy might be “lost,” meaning it doesn’t get transferred to the intended object in the form intended. Instead, it may have turned into heat energy, in overcoming friction.
6. A red wagon sits on the sidewalk. Joey pulls the wagon with a force of 50 newtons. When it has gone a distance of 4 meters the wagon has 170 joules of kinetic energy. How much work did Joey do on the wagon? How much KE did the wagon gain? How much work was done to overcome friction? (How much energy was “lost”?) Did that energy vanish? If not, where and in what form did it end up?