A 4.2 kg mass undergoes an acceleration given
by
~a = ax ˆı + ay ˆ ,
where ax = 0.6 m/s
2
and ay = 4.8 m/s
2
.
Find the magnitude of the resultant force.
Answer in units of N
To find the magnitude of the resultant force, we can use Newton's Second Law, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
In this case, we are given the mass of the object (m = 4.2 kg) and the acceleration vector (~a = ax ˆı + ay ˆ).
To find the magnitude of the resultant force, we need to calculate the magnitude of the acceleration vector:
|~a| = sqrt(ax^2 + ay^2)
Substituting the given values, we get:
|~a| = sqrt((0.6 m/s^2)^2 + (4.8 m/s^2)^2)
|~a| = sqrt(0.36 m^2/s^4 + 23.04 m^2/s^4)
|~a| = sqrt(23.4 m^2/s^4)
|~a| ≈ 4.834 m/s^2
Now, we can calculate the magnitude of the resultant force:
F = m * |~a|
F = 4.2 kg * 4.834 m/s^2
F ≈ 20.2716 kg⋅m/s^2
Since the unit of force is Newton (N), we can convert the unit:
1 N = 1 kg⋅m/s^2
F ≈ 20.2716 N
Therefore, the magnitude of the resultant force is approximately 20.2716 N.