the resistance of two forces are and 15 newton is 20 Newton in client at 60 angle to the 15 Newton force find the magnitude and direction
To find the magnitude and direction of the resultant force, we can use the method of vector addition. Given that one force is 15 Newtons and the other force is 20 Newtons with a 60-degree angle between them, we can proceed as follows:
Step 1: Break down the given forces into their horizontal and vertical components.
For the force of 15 Newtons:
Horizontal component = 15 * cos(0) = 15 * 1 = 15 Newtons
Vertical component = 15 * sin(0) = 15 * 0 = 0 Newtons
For the force of 20 Newtons:
Horizontal component = 20 * cos(60) = 20 * 0.5 = 10 Newtons
Vertical component = 20 * sin(60) = 20 * (√3/2) ≈ 17.3 Newtons
Step 2: Add up the horizontal and vertical components separately to obtain the resultant force.
Horizontal component of resultant force = 15 Newtons + 10 Newtons = 25 Newtons (towards the right)
Vertical component of resultant force = 0 Newtons + 17.3 Newtons = 17.3 Newtons (upwards)
Step 3: Use the Pythagorean theorem to find the magnitude of the resultant force.
Magnitude of resultant force = √(horizontal component^2 + vertical component^2)
= √(25^2 + 17.3^2)
≈ √(625 + 299.29)
≈ √924.29
≈ 30.4 Newtons (rounded to one decimal place)
Step 4: Calculate the direction of the resultant force.
Direction of the resultant force = tan^(-1)(vertical component / horizontal component)
= tan^(-1)(17.3 / 25)
≈ 34.7 degrees (rounded to one decimal place)
Therefore, the magnitude of the resultant force is approximately 30.4 Newtons, and its direction is approximately 34.7 degrees with respect to the horizontal axis.
To find the magnitude and direction of the resulting force, you can use vector addition. Here's how you can break it down:
1. Determine the horizontal and vertical components of each force:
- The 15 Newton force has a horizontal component of 15 Newton (cos 0°) and a vertical component of 0 Newton (sin 0°).
- The 20 Newton force has a horizontal component of 20 Newton (cos 60°) and a vertical component of 10 Newton (sin 60°).
2. Add up the horizontal and vertical components of the forces separately:
- Horizontal component: 15 Newton + 20 Newton × cos 60° = 15 Newton + 10 Newton = 25 Newton.
- Vertical component: 0 Newton + 20 Newton × sin 60° = 0 Newton + 10 Newton = 10 Newton.
3. Calculate the magnitude of the resulting force using the Pythagorean theorem:
- Magnitude (F) = √[(Horizontal component)^2 + (Vertical component)^2]
- F = √[(25 Newton)^2 + (10 Newton)^2]
- F ≈ √(625 Newton^2 + 100 Newton^2)
- F ≈ √725 Newton^2
- F ≈ 26.93 Newton.
4. Determine the direction of the resulting force using trigonometry:
- Direction (θ) = arctan(Vertical component / Horizontal component)
- θ = arctan(10 Newton / 25 Newton)
- θ ≈ arctan(0.4)
- θ ≈ 21.8°.
Therefore, the magnitude of the resulting force is approximately 26.93 Newton, and its direction is approximately 21.8°.