3. A dog sits 1 .50 m from the center of a merry -go-round and revolves at a tangential speed of 1.80m/s If the dog's mass is 18.5 kg , what is the magnitude of the centripetal force on the dog?

To find the magnitude of the centripetal force on the dog, we can use the formula for centripetal force:<br /><br />\[ F_c = \frac{mv^2}{r} \]<br /><br />where:<br />- \( m \) is the mass of the dog,<br />- \( v \) is the tangential speed of the dog,<br />- \( r is the radius of the circular path.<br /><br />Given:<br />- \( m = 18.5 \, \text{kg} \)<br />- \( v = 1.80 \, \text{m/s} \)<br />- \( r = 1.50 \, \text{m} \)<br /><br />Substituting these values into the formula:<br /><br />\[ F_c = \frac{18.5 \, \text{kg} \times (1.80 \, \text{m/s})^2}{1.50 \, \text{m}} \]<br /><br />First, calculate the tangential speed squared:<br /><br />\[ v^2 = (1.80 \, \text{m/s})^2 = 3.24 \, \text{m}^2/\text{s}^2 \]<br /><br />Next, multiply this by the mass of the dog:<br /><br />\[ mv^2 = 18.5 \, \text{kg} \times 3.24 \, \text{m}^2/\text{s}^2 = 60.42 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \]<br /><br />Finally, divide by the radius:<br /><br />\[ F_c = \frac{60.42 \, \text{kg} \cdot \text{m}^2/\text{s}^2}{1.50 \, \text{m}} = 40.28 \, \text{N} \]<br /><br />Therefore, the magnitude of the centripetal force on the dog is approximately \( 40.28 \, \text{N} \).