Question

A 1.5-kg mass has an acceleration of (4.0ˆi−3.0ˆj)m/s². Only two forces act on the mass. If one of the forces is (2.0ˆi−1.4ˆj)N, what is the magnitude of the other force?

a) 1.0 N

b) 2.0 N

c) 3.0 N

d) 4.0 N

Answer 1

To find the magnitude of the other force acting on the 1.5-kg mass, we can use the principle of Newton's second law. By setting up an equation using the known values, we can solve for the magnitude of the other force. The correct answer is 3.0 N (c).

Step-by-step explanation:

To find the magnitude of the other force acting on the 1.5-kg mass, we can use the principle of Newton's second law. According to this law, the sum of all the forces acting on an object is equal to the product of its mass and acceleration. So, the equation becomes:

F_net = m * a

In this case, we know the mass (1.5 kg) and the acceleration (4.0ˆi−3.0ˆj m/s²). Considering the forces acting on the object, one force is given as (2.0ˆi−1.4ˆj) N. Let's assume the magnitude of the other force is F₂ N.

So, F_net = F₁ + F₂, where F₁ is given as (2.0ˆi−1.4ˆj) N.

Substituting the known values into the equation, we have:

(2.0ˆi−1.4ˆj) N + F₂ N = (1.5 kg) * (4.0ˆi−3.0ˆj m/s²)

From this equation, we can solve for F₂, which will give us the magnitude of the other force acting on the mass.

Therefore, the correct answer is 3.0 N (c).