Question

Three forces act on an object, considered to be a particle, which moves with constant velocity v=(3ˆi−2ˆj)m/s. Two of the forces are →F1=(3ˆi+5ˆj)N and →F2=(4ˆi−7ˆj)N. Find the third force.

a) →F3 = (-4ˆi - 6ˆj) N
b) →F3 = (-1ˆi - 3ˆj) N
c) →F3 = (7ˆi - 2ˆj) N
d) →F3 = (1ˆi - 3ˆj) N

Answer 1

The third force acting on the particle must balance out the other two forces for the net force to be zero due to constant velocity. Summing the first two given forces results in (7î - 2æ) N, so the third force should be equal and opposite: (-7î + 2æ) N. Therefore, the correct answer is c) →F3 = (7ˆi - 2ˆj) N.

Step-by-step explanation:

To find the third force acting on a particle which moves with constant velocity, one must apply Newton's first law of motion. The law states that if a body is moving with constant velocity, the net force acting on it must be zero.

Since the particle in question moves with constant velocity v = (3î - 2æ)m/s and we are given two forces F1 = (3î + 5æ)N and F2 = (4î - 7æ)N, the third force F3 must be such that the sum of all three forces equals zero.

Summing the given forces:
F1 + F2 = (3 + 4)î + (5 - 7)æ = 7î - 2æ N.
To achieve a net force of zero, F3 must be the negative of this sum: F3 = -7î + 2æ N. Therefore, the third force is F3 = (-7î + 2æ) N, making option c) the correct answer.