Amass m=8,5 kg ball is swinging in a vertical circle of radius r=23cm If the constant speed of the ball is v=5m/s Determine the tension in the string at the bottom of the circle in units of N(Newton). Take g=9.8m/s^2 and round off your result to 1 decimal place. Yanit: square

To determine the tension in the string at the bottom circle, we need to consider both the centripetal force and the gravitational force acting on the ball.<br /><br />At the bottom of the circle, the tension in the string is the sum of the centripetal force and the gravitational force.<br /><br />The centripetal force can be calculated using the formula:<br /><br />$F_{c} = \frac{m \cdot v^2}{r}$<br /><br />where $m$ is the mass of the ball, $v$ is the constant speed of the ball, and $r$ is the radius of the circle.<br /><br />The gravitational force can be calculated using the formula:<br /><br />$F_{g} = m \cdot g$<br /><br />where $m$ is the mass of the ball and $g$ is the acceleration due to gravity.<br /><br />The total tension in the string at the bottom of the circle is the sum of the centripetal force and the gravitational force:<br /><br />$T = F_{c} + F_{g}$<br /><br />Substituting the given values:<br /><br />$F_{c} = \frac{8.5 \cdot 5^2}{0.23} = 859.13 \, \text{N}$<br /><br />$F_{g} = 8.5 \cdot 9.8 = 83.3 \, \text{N}$<br /><br />$T = 859.13 + 83.3 = 942.43 \, \text{N}$<br /><br />Rounding off to 1 decimal place, the tension in the string at the bottom of the circle is approximately 942.4 N.