When a force of 1 newton act on a mass of 1 kg which is able to move freely, the object moves in the direction of fore with a/an
Acceleration of 1 m/s 2
Understanding Newton's Second Law of Motion
This question involves a fundamental concept in physics: Newton's Second Law of Motion. This law describes how an object's motion changes when a force acts on it. It states that the acceleration of an object is directly proportional to the net force acting on it, is in the same direction as the net force, and is inversely proportional to its mass.
Mathematically, Newton's Second Law is expressed by the formula:
\(F = ma\)
Where:
- \(F\) is the net force acting on the object.
- \(m\) is the mass of the object.
- \(a\) is the acceleration of the object.
Calculating the Acceleration
The question gives us the following information:
- Force (\(F\)) = 1 Newton (N)
- Mass (\(m\)) = 1 kilogram (kg)
We need to find the acceleration (\(a\)). We can rearrange the formula \(F = ma\) to solve for acceleration:
\(a = \frac{F}{m}\)
Now, we can substitute the given values into this formula:
\(a = \frac{1 \text{ N}}{1 \text{ kg}}\)
To understand the units, recall that 1 Newton (N) is defined as the force required to accelerate a mass of 1 kilogram (kg) at a rate of 1 meter per second squared (m/s\(^2\)). So, \(1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2\).
Substituting the definition of Newton into our calculation:
\(a = \frac{1 \text{ kg} \cdot \text{m/s}^2}{1 \text{ kg}}\)
The kilogram units cancel out:
\(a = 1 \text{ m/s}^2\)
Analyzing the Options
Our calculation shows that a force of 1 Newton acting on a mass of 1 kg produces an acceleration of 1 m/s\(^2\). Let's look at the given options:
- Speed of 1 km/s: This option refers to speed, not acceleration. Newton's Second Law directly relates force to acceleration. Also, the unit is km/s, not m/s.
- Acceleration of 1 m/s \(^2\): This option refers to acceleration and the unit matches our calculation (1 m/s\(^2\)).
- Speed of 1 m/s: This option refers to speed, not acceleration.
- Acceleration of 1 km/s \(^2\): This option refers to acceleration, but the unit is km/s\(^2\), which is much larger than m/s\(^2\). 1 km/s\(^2\) is equal to 1000 m/s\(^2\).
Based on Newton's Second Law and our calculation, the object moves in the direction of the force with an acceleration of 1 m/s\(^2\).
Resulting Motion
When a force acts on an object, it causes the object to accelerate. Acceleration means the object's velocity (speed and direction) changes over time. In this case, the object starts from rest (assuming it was initially at rest or moving at a constant velocity before the force was applied) and its speed will increase by 1 m/s every second, in the direction of the force.
| Quantity | Value | Unit |
|---|---|---|
| Force (\(F\)) | 1 | Newton (N) |
| Mass (\(m\)) | 1 | kilogram (kg) |
| Calculated Acceleration (\(a\)) | 1 | meter per second squared (m/s\(^2\)) |
Revision Table: Key Concepts
| Concept | Definition | Standard Unit |
|---|---|---|
| Force | A push or pull that can cause an object to accelerate. | Newton (N) |
| Mass | A measure of the amount of matter in an object and its resistance to acceleration (inertia). | kilogram (kg) |
| Acceleration | The rate of change of velocity over time. It is a vector quantity. | meter per second squared (m/s\(^2\)) |
| Newton (Unit of Force) | 1 N is the force required to accelerate a mass of 1 kg at a rate of 1 m/s\(^2\). | kg⋅m/s\(^2\) |
Additional Information on Force, Mass, and Acceleration
Newton's Second Law, \(F=ma\), is fundamental to understanding classical mechanics. It highlights the direct relationship between force and acceleration (more force means more acceleration for the same mass) and the inverse relationship between mass and acceleration (more mass means less acceleration for the same force).
- Vector Nature: Force and acceleration are vector quantities, meaning they have both magnitude and direction. The acceleration is always in the same direction as the net force. Mass is a scalar quantity.
- Units: The standard units used in this calculation (Newton, kilogram, meter per second squared) belong to the International System of Units (SI). It is crucial to use consistent units when applying physics formulas.
- Speed vs. Acceleration: Speed is the magnitude of velocity (how fast something is moving). Acceleration is the rate at which speed or direction changes. A constant force causes constant acceleration, which in turn causes speed to change linearly over time.
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