A 1000-kg automobile is pulled by a horizontal tow line with a net force of 950 N. What is the acceleration of the auto? (Neglect friction.)
The correct answer and explanation is :
To find the acceleration of the automobile, we use Newton’s Second Law of Motion:
[
F = ma
]
where:
- ( F ) is the net force applied (950 N),
- ( m ) is the mass of the automobile (1000 kg),
- ( a ) is the acceleration (to be determined).
Rearranging the equation to solve for ( a ):
[
a = \frac{F}{m}
]
Substituting the given values:
[
a = \frac{950 \text{ N}}{1000 \text{ kg}}
]
[
a = 0.95 \text{ m/s}^2
]
Explanation:
The acceleration of the automobile is 0.95 m/s². This means that for every second the car is being pulled, its velocity increases by 0.95 meters per second in the direction of the applied force.
Newton’s Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Since we neglect friction, the only force affecting the car’s motion is the 950 N applied force.
If friction were present, the net force would be reduced by the frictional force, decreasing acceleration. But since we are given an ideal case with no friction, all 950 N contributes to acceleration.
The result shows that heavier objects require more force to accelerate at the same rate as lighter objects. If the car had a larger mass (e.g., 2000 kg), the acceleration would be lower, demonstrating how mass influences motion.
This principle is crucial in vehicle dynamics, engineering, and physics, affecting how engines are designed and how much force is needed to move different objects efficiently.