A 0.69 kg mass is observed to accelerate at 8.16 m/s2 in a direction 30.5° north of east. There is a force directed north acting on the object and a force directed east acting on the object. What is the magnitude of the force acting east on the object?
forceNorth= mass*accelerationNorth
forceEast= mass*acceleartionEast
so break up the acceleration in to N, and E components.
what are the conditions neccessary for a body to perform simple harmonic oscillation
To find the magnitude of the force acting east on the object, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
First, let's resolve the acceleration into its east and north components:
Acceleration in the east direction (a_east) = acceleration * cos(theta)
Acceleration in the north direction (a_north) = acceleration * sin(theta)
Given:
Mass (m) = 0.69 kg
Acceleration (a) = 8.16 m/s^2
Angle (theta) = 30.5°
Now, let's calculate the acceleration components:
a_east = 8.16 m/s^2 * cos(30.5°)
a_north = 8.16 m/s^2 * sin(30.5°)
Next, let's find the net force acting east on the object using Newton's second law:
Net force (F_east) = mass * acceleration in the east direction
F_east = 0.69 kg * a_east
Finally, we can calculate the magnitude of the force acting east:
Magnitude of force acting east = |F_east|
Now, let's substitute the values and solve the problem:
a_east = 8.16 m/s^2 * cos(30.5°) ≈ 7.087 m/s^2
F_east = 0.69 kg * 7.087 m/s^2 ≈ 4.890 N
Therefore, the magnitude of the force acting east on the object is approximately 4.890 Newtons.