18. A ball on a chain spins at 25m/s in a circular path with a radius of 60 meters. If the centripetal force of the ball is 550N, what is the mass of the ball?

To find the mass of the ball, we can use the formula for centripetal force:<br /><br />\[ F_c = \frac{mv^2}{r} \]<br /><br />where:<br />- \( F_c \) is the centripetal force,<br />- \( m \) is the mass of the ball,<br />- \( v \) is the velocity of the ball,<br />- \( r \) is the radius of the circular path.<br /><br />Given:<br />- \( F_c = 550 \, \text{N} \)<br />- \( v = 25 \, \text{m/s} \)<br />- \( r = 60 \, \text{m} \)<br /><br />We need to solve for \( m \):<br /><br />\[ m = \frac{F_c \cdot r}{v^2} \]<br /><br />Substitute the given values into the equation:<br /><br />\[ m = \frac{550 \, \text{N} \cdot 60 \, \text{m}}{(25 \, \text{m/s})^2} \]<br /><br />Calculate the denominator:<br /><br />\[ (25 \, \text{m/s})^2 = 625 \, \text{m}^2/\text{s}^2 \]<br /><br />Now, substitute back into the equation:<br /><br />\[ m = \frac{550 \, \text{N} \cdot 60 \, \text{m}}{625 \, \text{m}^2/\text{s}^2} \]<br /><br />\[ m = \frac{33000 \, \text{N} \cdot \text{m}}{625 \, \text{m}^2/\text{s}^2} \]<br /><br />\[ m = \frac{33000}{625} \, \text{kg} \]<br /><br />\[ m = 52.8 \, \text{kg} \]<br /><br />Therefore, the mass of the ball is \( 52.8 \, \text{kg} \).