A 10-kg duffle bag is undergoing a vertical acceleration of 0.050 m/s2 (positive for up, negative for down), while its owner is holding it with an upward force. What is the magnitude of this force?

force=mg+ma

105.5 To find the magnitude of the force exerted by the owner on the duffle bag, we need to consider the forces acting on the bag and apply Newton's second law of motion.

According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, this can be expressed as:

Fnet = m * a

In this case, the mass of the duffle bag (m) is given as 10 kg, and the vertical acceleration (a) is given as 0.050 m/s^2. We need to find the net force (Fnet).

Since the bag is undergoing vertical acceleration, there are two forces acting on it:
1. The gravitational force pulling it downward (weight) which can be calculated using the equation:
Fgravity = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. The upward force exerted by the owner (Fupward).

The net force can be calculated by subtracting the gravitational force from the upward force:
Fnet = Fupward - Fgravity

Since the duffle bag is not accelerating horizontally, we can assume that the net force is zero in the horizontal direction. Therefore, the upward force must exactly balance the gravitational force to prevent any horizontal motion.

So we have:
Fupward - Fgravity = 0

Rearranging the equation, we find:
Fupward = Fgravity

Substituting the values, we get:
Fupward = m * g = 10 kg * 9.8 m/s^2 = 98 N

Therefore, the magnitude of the force exerted by the owner on the duffle bag is 98 Newtons.