Answer:
a)11.25 J
b)Number of revolution = 1
Explanation:
Given that
Radius ,r= 0.8 m
m= 0.3 kg
Initial speed ,u= 10 m/s
final speed ,v= 5 m/s
a)
Initial energy
[tex]KE_i=\dfrac{1}{2}mu^2[/tex]
[tex]KE_i=\dfrac{1}{2}0.3\times 10^2[/tex]
KEi= 15 J
Final kinetic energy
[tex]KE_f=\dfrac{1}{2}mv^2[/tex]
[tex]KE_f=\dfrac{1}{2}0.3\times 5^2[/tex]
KEf=3.75 J
The energy transformed from mechanical to internal = 15 - 3.75 J = 11.25 J
b)
The minimum value to complete the circular arc
[tex]V=\sqrt{r.g}[/tex]
Now by putting the values
[tex]V=\sqrt{0.8\times 10}[/tex]
V= 2.82 m/s
So kinetic energy KE
[tex]KE=\dfrac{1}{2}mV^2[/tex]
[tex]KE=\dfrac{1}{2}0.3\times 2.82^2[/tex]
KE=1.19 J
ΔKE= KEi - KE
ΔKE= 15- 1.19 J
ΔKE=13.80 J
The minimum energy required to complete 2 revolutions = 2 x 11.25 J
= 22.5 J
Here 22.5 J is greater than 13.8 J.So the particle will complete only one revolution.
Number of revolution = 1
