A meteoroid passes between the moon and earth a gravitational force of 600N pulls the meteoroid toward the moon. At the same time, a gravitational force of 480N pulls the meteoroid toward the earth. The angle between the two forces is 130. The moons force ate perpendicular to the meteoroid original path.
What is the results magnitude and direction of the force acting on the meteoroid? State the direction in reference to the original path.
To find the resultant magnitude and direction of the force acting on the meteoroid, we can use the concept of vector addition. The gravitational forces in this scenario can be represented as vectors: one pointing towards the moon with a magnitude of 600N, and the other pointing towards the earth with a magnitude of 480N. The given angle between the two forces is 130°.
1. Draw a diagram: Start by drawing a diagram to visualize the situation. Draw a line to represent the original path of the meteoroid. Then, draw two arrows representing the gravitational forces towards the moon and the earth, respectively. Label each arrow with its magnitude.
2. Resolve the forces: We need to separate the given forces into their components along and perpendicular to the original path of the meteoroid. Since the moon's force is perpendicular to the original path, its component along the original path is zero. The earth's force has two components: one along the original path and one perpendicular to it. We can find the components using trigonometry.
- Component along the original path (Fx): Fx = 480N * cos(130°)
- Component perpendicular to the original path (Fy): Fy = 480N * sin(130°)
3. Add the components: Since the component perpendicular to the original path is not affecting the original path, we only need to consider the component along the original path. Both the force from the moon and the force from the earth act in the same direction along the original path of the meteoroid. Thus, we can add the two components together:
- Resultant force (Fresultant) = Fx (from earth's force) + Fmoon (from moon's force)
- Fresultant = Fx + 600N
4. Calculate the values: Substitute the values from step 2 and solve for the resultant magnitude of the force.
- Fresultant = (480N * cos(130°)) + 600N
- Fresultant ≈ -804.69N (Note: The negative sign indicates that the resultant force is in the opposite direction to the original path. The magnitude is approximately 804.69N.)
5. Determine the direction: Since the resultant force is negative, it means the force is acting in the opposite direction to the meteoroid's original path.
So, the resultant magnitude of the force acting on the meteoroid is approximately 804.69N, and the direction is opposite to the meteoroid's original path.