Respuesta :
Answer:
2.87 m
Explanation:
Given:
Mass of the ball (m) = 60 g = 0.06 kg
Height of the tube (h) = 0.70 m
Upward force by compressed air on the ball (F) = 3.0 N
Initial velocity of the ball (u) = 0 m/s (Assume)
Final velocity of the ball at the end of tube (v) Â = ?
Acceleration of the ball (a) = ?
Weight of the ball is equal to the product of mass and gravity. So,
Weight (W) = [tex]mg=0.06\times 9.8=0.588\ N[/tex]
Therefore, the net force acting on the ball is equal to the difference of upward force and downward force. So,
Net force = Force by air - Weight
[tex]F_{net}=F-mg\\F_{net}=3.0-0.588 = 2.412\ N[/tex]
Now, from Newton's second law, the net force is equal to the product of object's mass and acceleration. So,
[tex]F_{net}=ma\\\\a=\frac{F_{net}}{m}=\frac{2.412\ N}{0.06\ kg}=40.2\ m/s^2[/tex]
Now, acceleration (a) = 40.2 m/s²
Using equation of motion, we have:
[tex]v^2=u^2+2ah\\\\v^2=0+2\times 40.2\times 0.7\\\\v=\sqrt{56.28}=7.5\ m/s[/tex]
Now, let the maximum height reached be 'H'.
So, applying energy conservation from the top of pipe to the maximum height.
Decrease in kinetic energy = Increase in potential energy.
[tex]\frac{1}{2}mv^2=mgH\\\\H=\frac{v^2}{2g}[/tex]
Plug in the given values and solve for 'H'. This gives,
[tex]H=\frac{56.28}{2\times 9.8}\\\\H=\frac{56.28}{19.6}=2.87\ m[/tex]
Therefore, the ball reaches a height of 2.87 m above the top of the tube.
