Answer :
1) The gravitational potential energy of the child is 68 J
2) The child is 0.25 m above the ground
Explanation:
1)
The mechanical energy of a body is equal to the sum between its gravitational potential energy (PE) and its kinetic energy (KE):
[tex]E=PE+KE[/tex] (1)
In this problem, we know that
E = 315 J is the total mechanical energy of the child
Its kinetic energy is given by
[tex]K=\frac{1}{2}mv^2[/tex]
where
m = 28 kg is his mass
v = 4.2 m/s is his speed
Substituting,
[tex]K=\frac{1}{2}(28)(4.2)^2=247.0 J[/tex]
Substituting into (1), we can now find the potential energy of the child:
[tex]PE=E-KE=315-247=68 J[/tex]
2)
The gravitational potential energy of an object is given by
[tex]PE=mgh[/tex]
where
m is the mass
g is the gravitational acceleration
h is the height above the ground
For the child in this problem,
m = 28 kg
[tex]g=9.8 m/s^2[/tex]
and we know the value of its potential energy, PE = 68 J, therefore we can find his height above the ground:
[tex]h=\frac{PE}{mg}=\frac{68}{(28)(9.8)}=0.25 m[/tex]
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The potential energy of the child is 68 J.
We know that mechanical energy is the sum of the potential energy and the kinetic energy. First we need to obtain the kinetic energy of the body using the relation;
KE = 1/2mv^2 = 0.5 * 28 * (4.2)^2 = 247 J
Now;
Total Mechanical energy Kinetic energy + Potential energy
Potential energy = 315 J - 247 J = 68 J
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