during a football game two players try to tackle another player.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?and what is themagnitude and direction of the force
Total vector force = 50 i + 120 j
Total force magnitude = sqrt[(50)^2 + 120)^2] = 130 n
Total force direction = arctan(12/5) north of east. That would be 67.4 degrees in that direction
To find the total applied force, we need to add the two forces together. Since these forces are at right angles to each other, we can use the Pythagorean theorem to calculate the magnitude of the total force.
Step 1: Calculate the magnitude of the total force
Magnitude of the force applied by the first player (east): 50.0 N
Magnitude of the force applied by the second player (north): 120.0 N
Using the Pythagorean theorem, the magnitude of the total force can be calculated as follows:
Total force = √(Force1^2 + Force2^2)
= √((50.0 N)^2 + (120.0 N)^2)
= √(2500 + 14400)
= √16900
= 130 N (approximately)
Therefore, the magnitude of the total applied force is 130 Newtons.
Step 2: Calculate the direction of the total force
Since we have forces pushing in perpendicular directions, the total force can be represented as a vector in a Cartesian coordinate system. The angle can be found using trigonometry.
Angle θ = tan^(-1)(Force2 / Force1)
= tan^(-1)(120.0 N / 50.0 N)
≈ 67.38° (approximately)
Therefore, the direction of the total force is approximately 67.38° north of east.
To find the total applied force, we need to combine the individual forces applied by both players. Since the forces are applied in different directions (east and north), we can use vector addition to find the resultant force.
1. First, we represent each force as a vector. The force applied by the first player, 50.0 N to the east, can be represented as a vector pointing horizontally to the right. We'll call it F1 = 50.0 N (to the right).
The force applied by the second player, 120.0 N to the north, can be represented as a vector pointing vertically upwards. We'll call it F2 = 120.0 N (upwards).
2. Now, draw a coordinate plane with the x-axis representing east-west direction and the y-axis representing north-south direction.
3. Represent the first force, F1 = 50.0 N, as an arrow pointing to the right from the origin (0,0) on the x-axis.
Similarly, represent the second force, F2 = 120.0 N, as an arrow pointing upwards from the origin (0,0) on the y-axis.
4. The total applied force is the resultant of the two forces. To find it, we need to add the vectors F1 and F2 graphically.
5. To do this, draw a line from the tail of F1 to the tip of F2. This line represents the sum or resultant of the two forces.
6. Measure the length of the resultant line using a ruler or scale, and convert it to the appropriate unit (e.g., N).
7. The magnitude of the force can be found by using the Pythagorean theorem:
magnitude of the force = √(F1^2 + F2^2)
Substituting the given values:
magnitude of the force = √(50.0^2 + 120.0^2)
8. Calculate the magnitude using the equation stated above and determine the direction by measuring the angle the resultant vector makes with the positive x-axis. This can be done using a protractor or angle-measuring tool.
By following these steps, you can find the total applied force, its magnitude, and direction.