In an experiment, a boar (2600 kg) slows down from 11 m/s to 8 m/s in 5 sec when the engine is stopped.
a) Determine the drag force.
b) Using this information, what is a good approximation of the forward thrust force needed to keep the boat cruising at a constant speed of 9 to 10 m/s ?
Thank you so much!
To determine the drag force acting on the boat, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:
F = m * a
In this case, we know the mass of the boat is 2600 kg, and the boat slows down from 11 m/s to 8 m/s in 5 seconds. Since we're considering the deceleration, the acceleration is negative, so we have:
a = (final velocity - initial velocity) / time
a = (8 m/s - 11 m/s) / 5 s
a = -0.6 m/s^2
Now, we can use Newton's second law to find the force:
F = 2600 kg * (-0.6 m/s^2)
F = -1560 N
So, the drag force acting on the boat is 1560 Newtons.
Moving on to the second part of the question, it's essential to note that the drag force should balance with the forward thrust force in order to maintain a constant cruising speed. Therefore, to approximate the forward thrust force needed to keep the boat cruising at a speed of 9 to 10 m/s, we can assume that the drag force remains constant.
Considering a speed of 9 m/s, we know that the drag force is 1560 N. To maintain a constant speed, the forward thrust force should equal the drag force. Thus, the forward thrust force required is approximately 1560 N.
Similarly, for a speed of 10 m/s, we can use the same drag force value of 1560 N as an approximation for the forward thrust force needed to keep the boat cruising at a constant speed.
Please note that these approximations are reasonable estimates based on the assumption that the drag force remains constant over the speed range mentioned. In reality, drag forces can vary with changes in speed.