In the equation U g = m g y , the gravitational potential energy is directly proportional to the distance of the object from a planet. In the equation U g = − G m p m r , it is inversely proportional. How can you reconcile those two equations?
In the equation U g = m g y , the gravitational potential energy is directly proportional to the distance of the object from a planet. In the equation U g = − G m p m r , it is inversely proportional. How can you reconcile those two equations?
, the gravitational potential energy is directly proportional to the distance of the object from a planet. In the equation
U
g
=
−
G
m
p
m
r
, it is inversely proportional. How can you reconcile those two equations?
We are now able to define a mathematical formula for gravitational potential energy.
Near the Earth's surface, the gravitational potential energy of a system consisting of the earth and an object with a mass m is
EP = mgh,
where g is the acceleration of gravity (9.80 m/s2) and h is the height above ground level (positive upward).
Note that the "ground level" could really be any height we choose, because what's really important is the change in potential energy. The difference between two heights always gives the same change in potential energy, regardless of where we set the "zero" of height. In other words, if we find the change in potential energy
ΔEP = EP,f − EP,i,
the final potential energy minus the initial, we have
ΔEP = mghf − mghi = mgΔh.
The change in gravitational potential energy is just mg times the change in height.
Let's return to our ball-Earth example, only now let's examine a case where a ball is rising in the air.
You toss a ball with a mass of 0.703 kg upward.…
If a particle is moving, it has kinetic energy. Kinetic energy is the energy of motion, and it depends on the speed and mass of the particle. It is given by the formula
Ek = 1/2*mv2,
where
Ek
is the kinetic energy, m is the mass, and v is the speed of the particle.
The formula for kinetic energy has some important features to keep in mind.
Kinetic energy, and every other type of energy as well, is a scalar quantity, given by only a single number. Energy does not have a "direction", unlike a vector quantity. (This is in contrast to the vector quantity momentum, which you might have already studied.)
Kinetic energy, in particular, is always a positive number. (Note the speed v is the magnitude of the vector velocity, and therefore is positive. But even if it were a negative number, squaring it would always lead to a positive result.)
Kinetic energy depends on the square of the speed. (This is in contrast to the magnitude of momentum, mv, a quantity you may have already studied, which…
(a) Define kinetic energy and gravitational potential energy. What is the SI unit for energy?
(b) A ping-pong ball and a golf ball have the same speed. Which one will have the larger kinetic energy? Explain your answer. (c) A tennis ball is thrown upwards with sufficient speed to reach a height of 12 m.(i) What is the kinetic energy of the tennis ball at a height of 12 m?
(ii) Calculate the speed of the tennis ball when it reaches a height of 6 m.
(d) A 100 N force that makes an angle of 30o with the horizontal is used to move a 10 kg crate across a smooth floor. The crate moves through a distance of 500 cm. Find the work done by the force.
Chapter 7 Solutions
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