Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
When the cord carrying the ball is at 30 deg below horizontal, the ball is at
1.5 m - 0.70 sin 30 = 1.15 meters above ground
Energy of the ball at the topmost point of swing :
KE + PE = 1/2 m v² + m g h
= 1/2 0.160 3.26² + 0.160 * 9.81 * (1.50 + 0.70) = 8.767 Joules
Energy of the ball when the cord at 30 deg from horizontal
= 1/2 m V² + m g h =
= 1/2 * 0.160 V² + 0.160 * 9.81 * 1.15 = 0.08V² + 1.805 Joules
Conservation of energy : 0.08 V² + 1.805 = 8.767
V² = 87.025
V = 9.329 m/sec
1.5 m - 0.70 sin 30 = 1.15 meters above ground
Energy of the ball at the topmost point of swing :
KE + PE = 1/2 m v² + m g h
= 1/2 0.160 3.26² + 0.160 * 9.81 * (1.50 + 0.70) = 8.767 Joules
Energy of the ball when the cord at 30 deg from horizontal
= 1/2 m V² + m g h =
= 1/2 * 0.160 V² + 0.160 * 9.81 * 1.15 = 0.08V² + 1.805 Joules
Conservation of energy : 0.08 V² + 1.805 = 8.767
V² = 87.025
V = 9.329 m/sec
Answer:
The speed of the ball is 5.59 m/s.
Explanation:
Given that,
Mass = 0.160 kg
Radius = 70 cm =0.70 m
Distance = 1.50
Speed at top = 3.26 m/s
Angle = 30.0°
We need to calculate the speed of the ball
The total energy at the top
[tex]K.E_{i}+P.E=\dfrac{1}{2}mv_{i}^2+mgh[/tex]
The final kinetic energy of ball at that point when the cord is 30° below the horizontal
[tex]K.E_{f}=\dfrac{1}{2}mv_{f}^{2}[/tex]
Using conservation of energy
[tex]K.E_{f}=K.E_{i}+P.E[/tex]
[tex]\dfrac{1}{2}mv_{f}^2=\dfrac{1}{2}mv_{i}^2+mgh[/tex]
[tex]\dfrac{1}{2}\times0.160\times v_{f}^2=\dfrac{1}{2}\times0.160\times(3.26)^2+0.160\times9.8\times(0.70+0.70\times\sin30^{\circ})[/tex]
[tex]v_{f}=\sqrt{(3.26)^2+2\times9.8\times1.05}[/tex]
[tex]v_{f}=5.59\ m/s[/tex]
Hence, The speed of the ball is 5.59 m/s.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
