(1) The magnitude of the force that maintains circular motion acting on the puck is 14.7 N.
(2) The linear speed of the puck is 29.35 m/s.
The given parameters:
- Mass of air puck, m₁ = 0.029 kg
- Suspended mass, m₂ = 1.5 kg
- Radius of the circle, r = 1.7 m
The magnitude of the force that maintains circular motion acting on the puck;
[tex]F = \frac{m_1 v^2}{r}[/tex]
The tension on the string due to the suspended masse is calculated as follows;
[tex]T = m_2 g[/tex]
Since the two masses are in equilibrium;
[tex]\frac{m_1 v^2}{r} = m_2g\\\\m_1v^2 = m_2g r\\\\v^2 = \frac{m_2g r}{m_1} \\\\v= \sqrt{\frac{m_2g r}{m_1} } \\\\v = \sqrt{\frac{1.5 \times 9.8 \times 1.7}{0.029} } \\\\v = 29. 35 \ m/s[/tex]
The magnitude of the force that maintains circular motion acting on the puck;
[tex]F = \frac{m_1v^2}{r} \\\\F = \frac{0.029 \times (29.35)^2}{1.7} \\\\F = 14.7 \ N[/tex]
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