A sailboat, tied to a mooring with a line, weighs \(820 \mathrm{N}\) The mooring line pulls horizontally toward the west on the sailboat with a force of $110 \mathrm{N}$. The sails are stowed away and the wind blows from the west. The boat is moored on a still lake-no water currents push on it. Draw an FBD for the sailboat and indicate the magnitude of each force.

Short Answer

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Question: Draw a free body diagram for a sailboat weighing 820 N, tied horizontally towards the west with a mooring line exerting a force of 110 N, and with wind blowing from the west. Assume the boat is in a still lake with no water currents.

Step by step solution

01

Draw a free body diagram for the sailboat

To illustrate the forces acting on the sailboat, draw a simple sketch of the sailboat. Draw arrows representing the forces acting on the sailboat. Label each force accordingly.
02

Identify the forces acting on the sailboat

Identify the 3 main forces acting on the sailboat: 1. Gravitational Force (Weight): This force acts vertically downward, and its magnitude is equal to the weight of the sailboat (\(820 \mathrm{N}\)). In the FBD, draw an arrow pointing downward and label it as 'Weight = 820 N'. 2. Tension Force: This force represents the force exerted by the mooring line on the sailboat. It is mentioned that the mooring line pulls horizontally towards the west with a force of \(110 \mathrm{N}\). In the FBD, draw an arrow pointing to the left (towards the west) and label it as 'Tension = 110 N'. 3. Wind Force: The wind is blowing from the west, and it acts on the sailboat. Since the sails are stowed away, the force due to wind gets transferred to the boat through the mooring line. The wind force and tension force are equal and opposite. Since the boat remains in equilibrium, and there are no water currents affecting the boat, we can assume that the wind force acting on the boat is also \(110 \mathrm{N}\). In the FBD, draw an arrow pointing to the right (opposite of the tension force) and label it as 'Wind Force = 110 N'.
03

Indicate the magnitude of each force

In your FBD, you should now have three labeled arrows representing the forces acting on the sailboat. Make sure the magnitudes of the forces are clearly indicated: - Weight = 820 N (downwards) - Tension = 110 N (to the left, towards the west) - Wind Force = 110 N (to the right, opposite of the tension force) You have now successfully drawn a Free Body Diagram for the sailboat and indicated the magnitudes of all the forces acting on it.

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