Answer:
h = 0.25 [m]
v = 3.26 [m/s]
Explanation:
In order to solve this problem, we must remember that mechanical energy is defined as the sum of kinetic energy plus potential energy.
E1 = Ek + Ep
where:
E1 = mechanical energy = 25 [J]
Ek = kinetic energy = 17 [J]
Ep = potential energy [J]
25 = 17 + Ep
Ep = 8 [J]
Now the potential energy is defined by the following equation:
Ep = m*g*h
where:
m = mass = 3.2 [kg]
g = gravity acceleration = 9.81 [m/s²]
h = elevation [m]
8 = 3.2*9.81*h
h = 0.25 [m]
The velocity can be calculated by means of kinetic energy.
[tex]E_{k} =\frac{1}{2} *m*v^{2}\\17 =\frac{1}{2} *3.2*v^{2} \\v= \sqrt{\frac{17*2}{3.2} }\\v = 3.26[m/s][/tex]
(a) The height of the ball will be h=0.25 m
(b) The speed of the ball will be [tex]V= 3.26\ \frac{m}{s}[/tex]
It is given that
Mass of the ball m=-3.2kg
The kinetic energy of the ball = 17 j
The total mechanical energy of the ball = 25 J
(a) So the total mechanical energy is the sum of the kinetic energy of the ball and the potential energy of the ball.
[tex]E_T=E_{KE}+E_{PE}[/tex]
Now putting the values of the KE and the Total energy we get
[tex]25=17+E_{PE}[/tex]
[tex]E_{PE}=8 \ J[/tex]
Now the formula of the potential energy will be
[tex]E_{PE}=mgh[/tex]
[tex]8=3.2\times 9.81 \times h[/tex]
[tex]h= \dfrac{8}{3.2\times 9.81}[/tex]
[tex]h=0.25\ m[/tex]
(b) Now to find out the speed of the ball we have
[tex]E_K=17\ J[/tex]
[tex]E_K=\dfrac{1}{2} mv^2[/tex]
[tex]v=\sqrt{\dfrac{2E_{KE}}{m} }[/tex]
[tex]v=\sqrt{ \dfrac{2\times17}{3.2} }=3.25[/tex]
[tex]v=3.25 \ \dfrac{m}{s}[/tex]
So the calculated answers will be
(a) The height of the ball will be h=0.25 m
(b) The speed of the ball will be [tex]V= 3.26\ \frac{m}{s}[/tex]
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