How Do You Calculate a Boat's Acceleration on a Circular Path?

In summary, the boat has a circular path with a radius of 20m and a speed of 5m/s. The magnitude of its acceleration can be determined by using the equation a=(a(t)^2+a(n)^2)^1/2, where a(t)=2 and a(n)=v^2 / p. After plugging in these values, the boat's acceleration is calculated to be 2.36 m/s^2. The individual components of the acceleration, a(t) and a(n), are also provided.
  • #1
joemama69
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Homework Statement


A boat is traveling along a circular path having a radius of 20m. Determine the magnitude of the boat's acceleration when the speed is v=5m/s and the rate of increase in the speed is v'=2 m/s^2

Homework Equations



a=(a(t)^2+a(n)^2)^1/2

The Attempt at a Solution



I believe the a(t)=2 <--- May be wrong
and the equation for a(n)=v^2 / p which i got 1.25
so i pluged these into the relevant equation to get 2.36 m/s^2 is the magnitude of the boats acceleration
 
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  • #2
my question is if i did it right or not
 
  • #3
joemama69 said:
I believe the a(t)=2 <--- May be wrong
and the equation for a(n)=v^2 / p which i got 1.25
so i pluged these into the relevant equation to get 2.36 m/s^2 is the magnitude of the boats acceleration
Sounds good to me.
 

1. What is circular motion of a boat?

Circular motion of a boat refers to the movement of a boat along a curved path. This is typically seen when a boat is making a turn or navigating through a curved waterway.

2. What causes circular motion in a boat?

The circular motion of a boat is caused by the interaction between the boat's propeller and the water. The propeller creates a force that pushes the water in one direction, causing the boat to move in the opposite direction, resulting in a circular motion.

3. How do factors such as wind and current affect circular motion in a boat?

Factors such as wind and current can affect the circular motion of a boat by providing additional forces that can either assist or hinder the boat's movement. For example, a strong wind blowing in the same direction as the boat's circular motion can increase its speed, while a strong current pushing against the boat's motion can slow it down.

4. What is the difference between centripetal and centrifugal force in circular motion of a boat?

Centripetal force is the force that is acting towards the center of the circular motion, keeping the boat on its curved path. This force is provided by the boat's propeller. On the other hand, centrifugal force is the outward force that is experienced by the boat as it moves along the curved path. It is a result of the boat's inertia and is equal in magnitude but opposite in direction to the centripetal force.

5. How can the circular motion of a boat be controlled?

The circular motion of a boat can be controlled by adjusting the speed and direction of the boat's propeller. By increasing or decreasing the speed, the magnitude of the centripetal and centrifugal forces can be altered, thus changing the boat's circular motion. Additionally, steering the boat in a different direction can also change the circular path it follows.

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