a) Gravitational potential energy: 4.9 J
b) Kinetic energy: 4.9 J
c) Velocity of the ball: 4.4 m/s
d) Energy lost to friction: 1.0 J
Explanation:
a)
The gravitational potential energy of an object is the energy possessed by the object due to its position in the gravitational field. It is given by
where
m is the mass of the object
g is the acceleration due to gravity
h is the height relative to the ground
For the ball in this problem,
m = 0.5 kg
h = 1 m (the ball is at the 50-point ring)
Therefore, the potential energy is
b)
The mechanical energy of an object is given by the sum of potential energy (PE) and kinetic energy (KE):
where the kinetic energy is the energy due to the motion.
In absence of frictional force, the total mechanical energy of the ball is constant:
At the maximum height, the kinetic energy is zero (since the ball changes direction), so all the mechanical energy is potential energy:
However, when the ball is released, h = 0, so the potential energy is zero and all the mechanical energy is kinetic energy:
This means that
Therefore, the kinetic energy of the ball at its release is also 4.9 J.
c)
The kinetic energy of an object is given by
where
m is the mass of the object
v is its speed
In this problem, we have
m = 0.5 kg is the mass of the ball
KE = 4.9 J is the kinetic energy
Therefore, the velocity of the ball at its release is
d)
If the ball reaches only a height of h = 0.8 m, then its potential energy at the top is
This also means that the total mechanical energy at the top (h'=0.8 m) is
However, we are told that the kinetic energy of the ball when it is released is
So the mechanical energy at the release is
Therefore, the energy lost to friction is equal to the difference in energy:
Learn more about potential and kinetic energy:
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