Calculating Speedboat's Turn Dynamics

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SUMMARY

The discussion focuses on calculating the dynamics of a speedboat negotiating a circular turn with a radius of 32 meters. Key parameters include a speedboat length of 10.2 meters, a mass of 249 kg, and a net tangential force of 597 N applied by the engine. The initial speed of the boat is 4 m/s. The calculations required include tangential acceleration, tangential velocity, centripetal acceleration, and total acceleration at 2 seconds into the turn.

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Familiarity with circular motion dynamics
  • Knowledge of basic kinematics equations
  • Ability to calculate angular acceleration
NEXT STEPS
  • Calculate tangential acceleration using the formula: \( a_t = \frac{F}{m} \)
  • Determine tangential velocity after 2 seconds using \( v = u + a_t \cdot t \)
  • Calculate centripetal acceleration with \( a_c = \frac{v^2}{r} \)
  • Find total acceleration using vector addition of tangential and centripetal accelerations
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of vehicles in circular motion.

mattmannmf
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A speedboat with a length of 10.2m and a mass of 249 kg is negotiaging a circular turn (radius = 32 m) around a buoy. During the turn, the engine causes a net tangential force of magnitude 597 N to be applied to the boat. The intial speed of the boat going into the turn is 4 m/sec.
a) What is the tangential acceleration of the boat, 2 sec into the turn?

b) What is the tangential velocity of the boat, 2 sec into the turn?

c) What is the centripetal acceleration, 2 sec into the turn?

d) What is the total acceleration, 2 sec into the turn?

for a, Tan Accel= pi*angular acceleration. but i don't know really how to get started.
 
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mattmannmf said:
A speedboat with a length of 10.2m and a mass of 249 kg is negotiaging a circular turn (radius = 32 m) around a buoy. During the turn, the engine causes a net tangential force of magnitude 597 N to be applied to the boat. The intial speed of the boat going into the turn is 4 m/sec.
a) What is the tangential acceleration of the boat, 2 sec into the turn?

b) What is the tangential velocity of the boat, 2 sec into the turn?

c) What is the centripetal acceleration, 2 sec into the turn?

d) What is the total acceleration, 2 sec into the turn?

for a, Tan Accel= pi*angular acceleration. but i don't know really how to get started.

Maybe this will help?
http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html#rq
 

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