Calculating Force Required for Acceleration

This problem asks us to determine the amount of force needed to accelerate an object of a given weight at a specific rate. We are given the object's weight in Newtons (N) and the desired acceleration in meters per second squared (m/s²).

Understanding Weight and Mass

Before we can apply Newton's second law of motion (F=ma), which relates force, mass, and acceleration, we first need to find the object's mass. We are given its weight. Weight is the force of gravity acting on an object's mass. The relationship is given by:

$$ \text{Weight (W)} = \text{mass (m)} \times \text{acceleration due to gravity (g)} $$

The standard value for the acceleration due to gravity on Earth is approximately $9.8 \, \text{m/s}^2$.

Calculating the Object's Mass

We are given the weight (W) as 300 N. We can rearrange the formula above to solve for mass (m):

$$ m = \frac{W}{g} $$

Substituting the given weight and the approximate value for g:

$$ m = \frac{300 \, \text{N}}{9.8 \, \text{m/s}^2} $$

Let's perform the calculation:

So, the mass of the object is approximately 30.61 kg.

Applying Newton's Second Law to Find Force

Now that we have the mass of the object, we can use Newton's second law of motion to find the force required to accelerate it. Newton's second law states:

$$ \text{Force (F)} = \text{mass (m)} \times \text{acceleration (a)} $$

We are given the desired acceleration (a) as 2 m/s².

Substituting the calculated mass and the given acceleration into the formula:

$$ F = m \times a $$

$$ F = 30.61 \, \text{kg} \times 2 \, \text{m/s}^2 $$

Let's perform this calculation:

The force needed to accelerate the 300 N object at 2 m/s² is approximately 61.22 N.

Final Answer Derivation

Based on our calculations, the force required is 61.22 N. We converted the weight to mass using the relationship W=mg and then used Newton's second law F=ma to find the force. The options provided are:

• 150 N
• 30.61 N
• 61.22 N
• 15.31 N

Our calculated value matches one of the options.

Revision Table: Force and Motion Concepts

Additional Information: Newton's Laws

This problem directly applies Newton's second law of motion. Let's briefly look at all three of Newton's laws:

• Newton's First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force.
• Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The direction of the acceleration is in the direction of the net force. Mathematically represented as $$ F_{\text{net}} = m \times a $$.
• Newton's Third Law: For every action, there is an equal and opposite reaction. When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

Understanding these fundamental laws is crucial for solving problems involving force, mass, and motion.