If you've ever watched sailing, you will sometimes see a sailor hanging off the side of the boat, for example in this shot from the movie "The Thomas Crown Affair." Eventually, of course, the sailboat tips over so far that a person cannot keep it balanced. Consider an idealized model of a small sailboat where the boat is a point. We'll model the mast and sails as a 14 meter long uniform rod with total mass 400 kg. Our sailor will be modeled as a 100 kg point mass on the massless boom that extends 4 meters from the boat at a right angle to the sail. If θ is the angle between the mast and the horizontal axis, at what θ in degrees will the sailor be unable to keep the boat upright even if he is sitting at the end of the boom?
60
how did you do it
Right answer please
the answer is less than 60.
cheaters here will be suspended at brilliant.
81.87 is the answer.. :) promise!!!!
thanxxxxxxx hero.........
LOL its 80.8 don't listen to your hero
To determine the angle θ at which the sailor will be unable to keep the boat upright, we need to consider the torque acting on the boat-sailor system.
The torque is a measure of how much a force can cause an object to rotate. In this case, the torque exerted by the weight of the sailboat and the sailor must be balanced by the torque exerted by the sailor. When the torque balances, the boat will remain upright.
Let's break down the components of torque involved:
1. Torque exerted by the weight of the sailboat:
The weight of the sailboat can be considered as acting at the center of mass of the mast and sails. Let's assume the center of mass is located at a distance "d" from the rotation axis (point-like boat). The torque exerted by the weight is given by:
Torque_sailboat = Weight_sailboat * d
2. Torque exerted by the sailor:
The sailor is sitting at the end of the boom. Since the boom extends 4 meters from the boat, the distance from the rotation axis to the sailor is also 4 meters. The torque exerted by the sailor is given by:
Torque_sailor = Weight_sailor * 4
For the system to remain balanced, the torque exerted by the sailor must be equal to the torque exerted by the sailboat. Therefore, we can equate the torques:
Torque_sailboat = Torque_sailor
Weight_sailboat * d = Weight_sailor * 4
Now, let's substitute the given values:
Weight_sailboat = Mass_sailboat * g (where g is the acceleration due to gravity)
d = Length_of_mast_and_sails / 2 (assuming the center of mass is at the midpoint of the mast and sails)
Weight_sailor = Mass_sailor * g
Substituting these values, we get:
Mass_sailboat * g * (Length_of_mast_and_sails / 2) = Mass_sailor * g * 4
Simplifying the equation:
Mass_sailboat * Length_of_mast_and_sails = Mass_sailor * 8
Now, let's substitute the given masses and length:
400 kg * 14 m = 100 kg * 8
Simplifying the equation further:
5600 kg⋅m = 800 kg⋅m
Dividing both sides of the equation by 800 kg, we get:
7 m = 1 m
This is a contradiction! The equation is not consistent, which means that there is no value of θ at which the sailor will be unable to keep the boat upright.
Therefore, based on the provided information, the sailor will always be able to keep the boat upright regardless of the angle θ.