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Solution: A cannon is rigidly attached to a carriage, which
Chapter 9, Problem 70(choose chapter or problem)
A cannon is rigidly attached to a carriage, which can move along horizontal rails but is connected to a post by a large spring, initially unstretched and with force constant \(k=2.00 \times 10^{4} \mathrm{~N} / \mathrm{m}\), as shown in Figure P9.70. The cannon fires a 200-kg projectile at a velocity of 125 m/s directed \(45.0^{\circ}\) above the horizontal.
(a) Assuming that the mass of the cannon and its carriage is 5 000 kg, find the recoil speed of the cannon.
(b) Determine the maximum extension of the spring.
(c) Find the maximum force the spring exerts on the carriage.
(d) Consider the system consisting of the cannon, carriage, and projectile. Is the momentum of this system conserved during the firing? Why or why not?
Questions & Answers
QUESTION:
A cannon is rigidly attached to a carriage, which can move along horizontal rails but is connected to a post by a large spring, initially unstretched and with force constant \(k=2.00 \times 10^{4} \mathrm{~N} / \mathrm{m}\), as shown in Figure P9.70. The cannon fires a 200-kg projectile at a velocity of 125 m/s directed \(45.0^{\circ}\) above the horizontal.
(a) Assuming that the mass of the cannon and its carriage is 5 000 kg, find the recoil speed of the cannon.
(b) Determine the maximum extension of the spring.
(c) Find the maximum force the spring exerts on the carriage.
(d) Consider the system consisting of the cannon, carriage, and projectile. Is the momentum of this system conserved during the firing? Why or why not?
Step 1 of 5
A cannon is rigidly attached to a carriage, which can move along horizontal rails but is connected to a post by a large spring, initially unstretched and with force constant \(k=2.00 \times 10^{4} \mathrm{~N} / \mathrm{m}\), as shown in Figure P9.70.
The given values are,
Projectile mass \(m_{p}=200 \mathrm{~kg}\)
Canon mass \(m_{c}=5000 \mathrm{~kg}\)
projectile velocity \(v_{p}=125 \mathrm{~m} / \mathrm{s}\)
\(k=2 \cdot 10^{4} \mathrm{~N} / \mathrm{m}\)
force constant
\(\theta=45^{\circ}\) - projectile angle