At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
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.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.