An 800 kg police boat slows down uniformly from 50 km/h [E] to 20 km/h [E] as it enters a harbour. If the boat slows down over a 30 m distance, what is the force of friction on the boat? (Hint: You will need to convert the velocities into m/s.)
To go from km/h to m/s divide by 3.6 which is 1000 m/km / 3600 s/min
a = change in velocity/time (note it is negative)
F = m a
By the way, this ignores wave resistance which would be a major part of the retarding force.
Damon. can you answer in detail. I already converted. what do I do next.
To find the force of friction on the boat, we can use the equation of motion that relates the force of friction, mass, and acceleration.
Here's the step-by-step solution:
Step 1: Convert the given velocities from km/h to m/s.
- Velocity initial (vi) = 50 km/h
- Velocity final (vf) = 20 km/h
To convert km/h to m/s, divide the values by 3.6 (since 1 km/h = 1/3.6 m/s).
- vi = 50 km/h ÷ 3.6 = 13.89 m/s
- vf = 20 km/h ÷ 3.6 = 5.56 m/s
Step 2: Calculate the change in velocity (∆v).
∆v = vf - vi
= 5.56 m/s - 13.89 m/s
= -8.33 m/s (Note: The negative sign indicates that the boat is slowing down.)
Step 3: Calculate the acceleration (a).
Using the equation of motion v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
- Rearranging the equation, a = (v^2 - u^2) / (2s)
a = (∆v^2) / (2s)
= (-8.33 m/s)^2 / (2 * 30 m)
≈ 15.22 m/s^2 (rounded to two decimal places)
Step 4: Calculate the force of friction (F).
Using the equation F = ma, where m is the mass of the boat (800 kg) and a is the acceleration.
- Substitute the values into the equation:
F = 800 kg * 15.22 m/s^2
≈ 12,177.60 N (rounded to two decimal places)
Therefore, the force of friction on the boat is approximately 12,177.60 N.