Question

Force of \(5 \mathrm{~N}\) acts on a body of weight \(9.8 \mathrm{~N}\). what is the acceleration produced in \(\mathrm{ms}^{-2}\). (A) \(49.00\) (B) \(5.00\) (C) \(1.46\) (D) \(0.51\)

Short answer

(B) 5.00

Step-by-step solution

Convert weight to mass

In order to determine the mass of the object, we need to convert the weight from newtons (N) to mass in kilograms (kg). Since weight is the force of gravity acting on an object (mass x acceleration due to gravity), we can write: Weight = mass × gravitational acceleration So, we can find the mass by: Mass = Weight / gravitational acceleration Where: Weight = 9.8 N Gravitational acceleration ≈ 9.8 m/s² Inserting the values, we get: Mass (in kg) = \( \frac {9.8 \mathrm{~N}}{9.8 \mathrm {~m/s}^2} = 1 \mathrm{~kg}\)

Calculate the acceleration using Newton's second law

Now, we will apply Newton's second law of motion to calculate the acceleration produced from the given force. The formula for Newton's second law is: Force = Mass × Acceleration Rearranging the formula to find the acceleration: Acceleration = \( \frac{Force}{Mass}\) Where: Force = 5 N Mass = 1 kg Substitute the values: Acceleration = \( \frac{5 \mathrm{~N}}{1 \mathrm{~kg}} = 5 \mathrm{~m/s^2}\)

Find the answer in the given options

The calculated acceleration is 5 m/s², which corresponds to option (B) from the given options. So, the correct answer is: (B) 5.00

Key concepts

Force

Force is a fundamental concept in physics, representing the push or pull on an object that can cause it to accelerate, slow down, remain in place, or change direction. Force is measured in newtons (N) and is a vector quantity, which means it has both magnitude and direction.

In the problem, we are given a force of 5 N acting on a body, which is used to calculate the acceleration of the body. The relation between force and motion is eloquently captured in Newton's Second Law of Motion, which states that the force applied on an object is directly proportional to the acceleration it produces. This is mathematically expressed as:

\[ \text{Force} = \text{Mass} \times \text{Acceleration} \]

This formula tells us that for a constant force, an increase in mass will lead to a decrease in acceleration, and vice versa. Understanding force is key to predicting how objects will move in a variety of situations.

Acceleration

Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity, measured in meters per second squared (m/s²). If an object speeds up, slows down, or changes direction, it is accelerating.

Using Newton's Second Law, once we know the force applied and the mass of the object, we can calculate acceleration with the formula:

\[ \text{Acceleration} = \frac{\text{Force}}{\text{Mass}} \]

In our given problem, applying a force of 5 N on a mass of 1 kg results in an acceleration of 5 m/s². This means the velocity of the object increases by 5 meters per second every second in the direction of the applied force.

Acceleration plays a pivotal role in understanding the dynamics of motion, allowing for predictions about how fast objects will move or stop under given forces.

Mass Conversion

Mass conversion is often necessary in physics problems, especially when dealing with forces and accelerations. The mass of an object is a measure of how much matter it contains and is typically measured in kilograms (kg) in the metric system.

In the exercise, we needed to convert the weight of the object into mass because weight is the force due to gravity acting on the mass of the object. Using the formula for weight (Weight = Mass × Gravitational Acceleration), we can rearrange to find mass:

\[ \text{Mass} = \frac{\text{Weight}}{\text{Gravitational Acceleration}} \]

For this problem, with a weight of 9.8 N and standard gravitational acceleration of 9.8 m/s², the mass of the object is calculated to be 1 kg. Correct mass conversion is crucial for accurately applying Newton's Second Law to calculate the resulting acceleration.

Gravitational Acceleration

Gravitational acceleration is the acceleration of an object due to the earth's gravity. On earth, it is approximately 9.8 m/s². This means that, in free fall, an object's velocity would increase by 9.8 meters per second every second, if air resistance is negligible.

In our problem, gravitational acceleration is used to convert weight to mass. Weight is the gravitational force acting on an object's mass, and using the gravitational acceleration value helps us determine how much matter the object actually contains (its mass).

This concept is vital for solving many physics problems, as weight and mass are interconnected through gravitational acceleration. Understanding how gravity affects objects around us helps explain phenomena ranging from falling objects to planetary orbits.