The wind exerts a force of 305 N North on
a sailboat, while the water exerts a force of
123 N West on the sailboat.
What is the magnitude of the net external
force on the sailboat?
Answer in units of N
To find the magnitude of the net external force on the sailboat, we need to combine the forces exerted by the wind and the water. Since the forces are acting in different directions, we can calculate the net force by using vector addition.
We can use the Pythagorean theorem to find the magnitude of the net force. The magnitude of the net force is given by the square root of the sum of the squares of the individual forces.
Net force = √(force of wind^2 + force of water^2)
= √(305^2 + 123^2)
= √(93025 + 15129)
= √108154
≈ 328.9 N
Therefore, the magnitude of the net external force on the sailboat is approximately 328.9 N.
To determine the magnitude of the net external force on the sailboat, we need to find the vector sum of the forces exerted by the wind and water.
Step 1: Convert the forces into vector notation.
The force exerted by the wind is given as 305 N North, so we represent it as a vector F_wind = 305 N North.
The force exerted by the water is given as 123 N West, so we represent it as a vector F_water = 123 N West.
Step 2: Add the vectors to find the net force.
To add the vectors, we need to break them down into their horizontal (x) and vertical (y) components. The x-axis represents the West-East direction, and the y-axis represents the North-South direction.
For F_wind = 305 N North, the y-component is 305 N, and the x-component is 0 N.
For F_water = 123 N West, the y-component is 0 N, and the x-component is -123 N.
Now, we add the x-components and the y-components separately:
Fx = 0 N + (-123 N) = -123 N
Fy = 305 N + 0 N = 305 N
Step 3: Find the magnitude of the net force.
To find the magnitude (or the absolute value) of the net force, we use the Pythagorean theorem.
Magnitude of the net force (Fnet) = √(Fx^2 + Fy^2)
Fnet = √((-123 N)^2 + (305 N)^2)
Fnet ≈ √(15129 N^2 + 93025 N^2)
Fnet ≈ √108154 N^2
Fnet ≈ 329 N.
Therefore, the magnitude of the net external force on the sailboat is approximately 329 N.