During a football game, two players try to tackle another play. One player applies a force of 50.0 N to the east. A second player applies a force of 120.0 N to the north. What is the total applied force? (Since force is a vector, you must give both the magnitude and direction of the force.)
Are they tackling a play or a player?
If a player, perform a vector addition of the two forces.
The Pythagorean theorem can be used here, since the separate forces are perpendicular
To find the total applied force, we need to use vector addition. Vector addition involves adding the magnitudes of the forces and considering their directions.
In this scenario, one player applies a force of 50.0 N to the east, and the other player applies a force of 120.0 N to the north. To add these vectors, we first need to break them down into their horizontal (x) and vertical (y) components.
For the force of 50.0 N to the east, the x-component is positive (east) and the y-component is zero since there is no force in the north-south direction.
For the force of 120.0 N to the north, the x-component is zero since there is no force in the east-west direction, and the y-component is positive (north).
Now, let's calculate the x and y components separately:
The x-component of the total force is the sum of the x-components of each force. So, the x-component is 50.0 N (east).
The y-component of the total force is the sum of the y-components of each force. So, the y-component is 120.0 N (north).
Now we have the x-component and y-component of the total force. To find the magnitude and direction of the total force, we can use the Pythagorean theorem and trigonometry.
The magnitude of the total force (F) is given by the equation:
F = √(Fx² + Fy²)
Substituting the x and y components we calculated earlier:
F = √((50.0 N)² + (120.0 N)²)
Calculating this expression gives us the magnitude of the total force:
F ≈ 130.42 N
To find the direction of the total force (θ), we can use the tangent function:
θ = tan^(-1)(Fy/Fx)
Substituting the x and y components:
θ = tan^(-1)((120.0 N) / (50.0 N))
Calculating this expression gives us the direction of the total force:
θ ≈ 67.38 degrees
Therefore, the total applied force is approximately 130.42 N directed at an angle of 67.38 degrees from the positive x-axis.