A particle with mass
m = 3.80 kg
accelerates according to
a = (−2.60i + 1.70j) m/s2.
(a) What is the net force acting on the particle? (Express your answer in vector form.)
F =
N
(b) What is the magnitude of this force?
N
To calculate the net force acting on a particle, we need to use Newton's second law of motion which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given:
mass, m = 3.80 kg
acceleration, a = (-2.60i + 1.70j) m/s^2
(a) To find the net force, we multiply the mass by the acceleration vector. Since the acceleration is given in vector form, we need to multiply the corresponding components separately.
F = m * a
= (3.80 kg) * (-2.60i + 1.70j)
= (-9.77i + 6.46j) N
So, the net force acting on the particle is F = (-9.77i + 6.46j) N.
(b) To find the magnitude of this force, we can use the Pythagorean theorem. The magnitude of a vector F = (Fx, Fy) can be calculated as follows:
|F| = sqrt(Fx^2 + Fy^2)
Therefore, the magnitude of the force is:
|F| = sqrt((-9.77)^2 + (6.46)^2) N
= sqrt(95.52 + 41.8916) N
= sqrt(137.4116) N
= 11.72 N (rounded to two decimal places)
So, the magnitude of the force is 11.72 N.
Force= mass*acceleration
so multiply acceleration by mass.
Force magnitude: the two components, each squared, added, in ... such a manner if
force= xxxi + yyyj then
force=sqrt(XXX^2 + YYY^2)