21.At the airport, a person pushes a luggage cart with an applied force of 150 N [forward]. Assuming the cart and luggage have a total mass of 46.0 kg and the force of friction is 95.0 N [backward], the magnitude of the acceleration of the luggage is _____ m/s2.
To find the magnitude of the acceleration of the luggage, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass:
acceleration = (net force) / (mass)
In this case, the net force is the applied force minus the force of friction:
net force = applied force - force of friction
Given:
Applied force = 150 N [forward]
Force of friction = 95 N [backward]
Total mass of cart and luggage = 46.0 kg
To find the net force, subtract the force of friction from the applied force:
net force = 150 N - 95 N = 55 N [forward]
Now we can substitute the values into the formula to calculate the acceleration:
acceleration = (55 N) / (46.0 kg)
Using a calculator, we can divide 55 by 46.0 to find the magnitude of the acceleration. The result is approximately 1.20 m/s².
Therefore, the magnitude of the acceleration of the luggage is approximately 1.20 m/s².