What will be the acceleration produced when a force of 21 N is applied on an object of mass 3 kg?
7ms -2
Calculating Acceleration Using Newton's Second Law
This problem involves finding the acceleration of an object when a force is applied to it. This is a classic application of Newton's Second Law of Motion, which describes the relationship between force, mass, and acceleration.
Understanding Newton's Second Law of Motion
Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting upon it, is in the same direction as the net force, and is inversely proportional to the mass of the object. Mathematically, this is expressed by the formula:
$$ F = ma $$
Where:
- \( F \) is the net force applied (measured in Newtons, N)
- \( m \) is the mass of the object (measured in kilograms, kg)
- \( a \) is the acceleration produced (measured in meters per second squared, m/s²)
In this question, we are given the force and the mass, and we need to find the acceleration. We can rearrange the formula to solve for acceleration:
$$ a = \frac{F}{m} $$
Applying the Formula to Find Acceleration
We are given:
- Force, \( F = 21 \) N
- Mass, \( m = 3 \) kg
Now, we can substitute these values into the rearranged formula:
$$ a = \frac{21 \text{ N}}{3 \text{ kg}} $$
Performing the division:
$$ a = 7 \frac{\text{N}}{\text{kg}} $$
The unit N/kg is equivalent to m/s². This is because 1 Newton is defined as the force required to accelerate a 1-kilogram mass at a rate of 1 meter per second squared ($$ 1 \text{ N} = 1 \text{ kg} \cdot 1 \text{ m/s}^2 $$). Therefore, N/kg = (kg · m/s²) / kg = m/s².
So, the acceleration is:
$$ a = 7 \text{ m/s}^2 $$
Analyzing the Options
Let's compare our calculated acceleration with the given options:
| Option | Value | Comparison |
|---|---|---|
| 1 | $$ 0.007 \text{ m/s}^2 $$ | Does not match our calculated value. |
| 2 | $$ 0.7 \text{ m/s}^2 $$ | Does not match our calculated value. |
| 3 | $$ 7 \text{ m/s}^2 $$ | Matches our calculated value. |
| 4 | $$ 70 \text{ m/s}^2 $$ | Does not match our calculated value. |
The calculated acceleration of 7 m/s² matches the value given in Option 3.
Conclusion on Acceleration Calculation
When a force of 21 N is applied to an object with a mass of 3 kg, the acceleration produced is 7 m/s². This result is obtained directly from Newton's Second Law of Motion, \( a = F/m \).
Revision Table: Key Physics Concepts
| Concept | Description | Formula |
|---|---|---|
| Force | A push or pull that can cause a change in an object's motion. Measured in Newtons (N). | $$ F = ma $$ |
| Mass | A measure of the amount of matter in an object. It resists changes in motion (inertia). Measured in kilograms (kg). | $$ m = F/a $$ |
| Acceleration | The rate of change of velocity of an object. Measured in meters per second squared (m/s²). | $$ a = F/m $$ |
| Newton's Second Law | The net force on an object is equal to the rate of change of its momentum; if mass is constant, $$ F = ma $$. | $$ F_{net} = ma $$ |
Additional Information on Force, Mass, and Acceleration
Force, mass, and acceleration are fundamental concepts in classical mechanics. It's important to remember:
- Force is a Vector: Force has both magnitude (size) and direction. Acceleration is also a vector and is always in the same direction as the net force. Mass is a scalar quantity, meaning it only has magnitude.
- Units: The standard units (SI units) are essential for calculations. Force in Newtons (N), mass in kilograms (kg), and acceleration in meters per second squared (m/s²). Using these units ensures the formula \( F=ma \) works correctly.
- Net Force: Newton's Second Law uses the net force, which is the vector sum of all individual forces acting on the object. In this problem, we assumed the 21 N was the only force or the net force.
- Constant Mass: The formula \( F=ma \) is most directly applied when the mass of the object remains constant during the acceleration.
Understanding these concepts helps in solving a wide range of physics problems involving motion and forces.
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