A particle with mass m = 3.80 kg accelerates according to
a = (−2.70i + 1.90j) m/s2.
What is the magnitude of this force?
F = ma
you want |F| as usual
To find the magnitude of the force, we can use Newton's second law. According to Newton's second law:
F = m * a
where F is the force, m is the mass, and a is the acceleration.
Given that the mass of the particle is m = 3.80 kg and the acceleration is a = (-2.70i + 1.90j) m/s^2, we can substitute these values into the formula to find the magnitude of the force.
F = (3.80 kg) * (-2.70i + 1.90j) m/s^2
To find the magnitude of a vector, we use the formula:
|v| = sqrt(vx^2 + vy^2)
where |v| is the magnitude of the vector, and vx and vy are the x and y components of the vector.
Therefore, we can calculate the magnitude of the force as follows:
|F| = sqrt((-2.70)^2 + (1.90)^2) m/s^2
|F| = sqrt(7.29 + 3.61) m/s^2
|F| = sqrt(10.90) m/s^2
|F| ≈ 3.30 m/s^2
Therefore, the magnitude of the force is approximately 3.30 m/s^2.