1) The ball has kinetic energy and it is 0.045 J
2) The ball has potential energy and it is 0.196 J
3) The volleyball has kinetic energy and it is 945 J
4) The carriage has potential energy and it is [tex]4.12\cdot 10^5 J[/tex]
Explanation:
1)
The kinetic energy of an object is the energy possessed by the object due to its motion. Mathematically, it is given by
[tex]KE=\frac{1}{2}mv^2[/tex]
where
m is the mass of the object
v is its speed
In this part of the problem, we have a rolling ball: since the ball is in motion, it has kinetic energy. The ball has
m = 10 g = 0.010 kg is its mass
v = 3 m/s is its speed
So, its kinetic energy is
[tex]KE=\frac{1}{2}(0.010)(3)^2=0.045 J[/tex]
2)
The gravitational potential energy is the energy possessed by an object due to its height above the ground, and it is given by
[tex]PE=mgh[/tex]
where
m is the mass of the object
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
h is the height of the object above the ground
In this part of the problem, the ball is located above the ground, so it has potential energy. The data for the ball are
m = 10 g = 0.010 kg is its mass
h = 2 m is its height above the ground
Substituting,
[tex]PE=(0.010)(9.8)(2)=0.196 J[/tex]
3)
As in part 1, the volleyball in this part is moving, so it has kinetic energy. It can be calculated as
[tex]KE=\frac{1}{2}mv^2[/tex]
where
m is the mass of the ball
v is its speed
Here we have
m = 2100 g = 2.1 kg
v = 30 m/s
Substituting, we find the kinetic energy of the ball:
[tex]KE=\frac{1}{2}(2.1)(30)^2=945 J[/tex]
4)
As in part 2, the carriage is located at a certain height above the ground, therefore it has potential energy, given by
[tex]PE=mgh[/tex]
where
m is the mass of the carriage
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
h is the height of the carriage above the ground
Here we have
m = 2000 kg is the mass
h = 21 m is the height
Substituting,
[tex]PE=(2000)(9.8)(21)=4.12\cdot 10^5 J[/tex]
Learn more about kinetic and potential energy:
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