Two horizontal forces, and , are acting on a box, but only is shown in the drawing. can point either to the right or to the left. The box moves only along the x axis. There is no friction between the box and the surface. Suppose that = +8.3 N and the mass of the box is 4.5 kg. Find the magnitude and direction of when the acceleration of the box is (a) +6.1 m/s2, (b) -6.1 m/s2, and (c) 0 m /s2.

Bill, please clarify your problem by adding the missing words.

Fnet= F1 + F2

Fnet=mass * acceleration

+8.3+ F2= (4.5)a

A) F2= (4.5)(+6.1) - 8.3
B) F2= (4.5)(-6.1) - 8.3
C) F2= 0 - 8.3

To find the magnitude and direction of the horizontal force when the acceleration of the box is given, we can use Newton's second law of motion:

Force (F) = mass (m) × acceleration (a)

Given:
Acceleration (a) = 6.1 m/s²

(a) To find the magnitude and direction of the force when the acceleration is +6.1 m/s²:
Mass (m) = 4.5 kg

Using the equation F = m × a, we can substitute the values and solve for the force:

F = (4.5 kg) × (6.1 m/s²)
F = 27.45 N

Therefore, the magnitude of the force is 27.45 N.

(b) To find the magnitude and direction of the force when the acceleration is -6.1 m/s²:
Since the acceleration is in the opposite direction, the force must also be in the opposite direction to cause the deceleration. Therefore, the force should be pointing to the left.

Using the same equation, we can substitute the given values:

F = (4.5 kg) × (-6.1 m/s²)
F = -27.45 N

Therefore, the magnitude of the force is 27.45 N, and it is pointing to the left.

(c) To find the magnitude and direction of the force when the acceleration is 0 m/s²:
If the acceleration is zero, the net force acting on the box must also be zero since the box is not accelerating. Therefore, the two forces acting on the box must be equal in magnitude but opposite in direction.

The force is given as +8.3 N. Therefore, must be equal in magnitude but pointing in the opposite direction, i.e., -8.3 N, to cancel out the net force and result in zero acceleration.

Therefore, the magnitude of when the acceleration is 0 m/s² is 8.3 N, and it is pointing to the left.