A 1.3 kg mass accelerates at 8.2 m/s2
in a direction 23 degrees north of east. One of the two forces acting on the mass has a magnitude of 7.85 N and is directed north.Determine the magnitude of the second force.
Im in need of serious help I only have one try left
To solve this problem, we can break down the given information into components and apply Newton's second law of motion.
1. Break down the given information:
Given:
- Mass (m) = 1.3 kg
- Acceleration (a) = 8.2 m/s^2
- Angle (θ) = 23 degrees (north of east)
- Force 1 (F1) = 7.85 N, directed north
Unknown:
- Force 2 (F2)
2. Resolve the given force into its components:
Since Force 1 is directed north and the angle θ is measured north of east, we need to find the north and east components of this force.
The north component (F1north) can be found by multiplying the magnitude of Force 1 (F1) with the cosine of the angle θ.
F1north = F1 * cos(θ)
F1north = 7.85 N * cos(23°)
F1north = 7.23 N
The east component (F1east) can be found by multiplying the magnitude of Force 1 (F1) with the sine of the angle θ.
F1east = F1 * sin(θ)
F1east = 7.85 N * sin(23°)
F1east = 3.34 N
3. Determine the net force:
Since we have the acceleration and mass, we can calculate the net force using Newton's second law of motion:
Fnet = m * a
Fnet = 1.3 kg * 8.2 m/s^2
Fnet = 10.66 N
4. Apply the principle of vector addition:
Since we have the north and east components of Force 1 and the net force, we can find the second force (F2) by subtracting the components of Force 1 from the net force.
F2 = Fnet - F1
To find the magnitude (|F2|) of Force 2:
|F2| = sqrt[(F2north)^2 + (F2east)^2]
Plug in the given values:
|F2| = sqrt[(10.66 N - 7.23 N)^2 + (0 - 3.34 N)^2]
|F2| = sqrt[(3.43 N)^2 + (-3.34 N)^2]
|F2| = sqrt[11.79 N^2 + 11.12 N^2]
|F2| = sqrt[22.91 N^2]
|F2| = 4.79 N
Therefore, the magnitude of the second force (F2) is 4.79 N.