The Correct Answer and Explanation is:
Correct Answer: 15.0 Newtons
Explanation:
The problem asks for the amount of force required to accelerate an object. To find this, we use the fundamental principle of classical mechanics known as Newton’s Second Law of Motion. This law establishes a direct relationship between the force applied to an object, its mass, and the acceleration it experiences. The law is expressed by the mathematical formula F = ma, where F represents the net force, m stands for the mass of the object, and a is the resulting acceleration.
Before we can apply this formula, it is crucial to ensure that all our values are in the correct standard international (SI) units. The standard unit for force is the Newton (N), for mass it is the kilogram (kg), and for acceleration it is meters per second squared (m/s²).
The problem provides the mass of the object as 1500 grams (g). As the problem instruction correctly points out, we must first convert this mass from grams to kilograms to maintain consistency within the formula. Since there are 1000 grams in 1 kilogram, we perform the following conversion:
Mass (m) = 1500 g / 1000 = 1.5 kg
Now we have the mass in the proper unit. The problem also gives us the acceleration directly in the correct SI unit:
Acceleration (a) = 10.0 m/s²
With both mass and acceleration in their standard units, we can substitute these values into Newton’s Second Law formula:
F = ma
F = (1.5 kg) × (10.0 m/s²)
F = 15.0 kg·m/s²
The resulting unit, kilograms times meters per second squared (kg·m/s²), is the definition of a Newton (N). Therefore, the amount of force applied to the object is 15.0 Newtons. The use of “10.0” in the problem implies a precision to three significant figures, so the answer is appropriately stated as 15.0 N.
