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?
To find the magnitude of the force, we need to consider the forces acting on the duffle bag and apply 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.
In this case, the forces acting on the duffle bag are the gravitational force pulling it downward and the upward force exerted by the owner. Since the duffle bag is undergoing a vertical acceleration, we can assume it is being accelerated vertically and the net force is the difference between these two forces.
Let's consider the direction of the forces. The gravitational force is acting downward, so we can represent it as -mg (negative sign indicating downward). The force exerted by the owner is acting upward, so we can represent it as +F (positive sign indicating upward).
Now, using Newton's second law of motion, we have:
net force = mass x acceleration
The net force is the sum of the gravitational force and the force exerted by the owner, so:
(-mg) + F = m x (0.050 m/s^2)
Now, we can solve for the magnitude of the force (F):
F = m x (0.050 m/s^2) + mg
Substituting the values given:
F = (10 kg) x (0.050 m/s^2) + (10 kg) x (9.8 m/s^2)
Calculating:
F = 0.5 N + 98 N
F = 98.5 N
Therefore, the magnitude of the force exerted by the owner on the duffle bag is 98.5 Newtons.