A 450 Kg Piano Has An Acceleration Of $+6.0 \, \text{m/s}^2$ When A Force Is Exerted On It. What Is The Net Force Acting On The Piano?Hint: Use The Formula $F = Ma$. Remember To Indicate The Direction (+ Or -) And Magnitude.

Feb 25, 2025 by ADMIN 225 views

A 450 kg Piano Accelerates Under Force: Calculating the Net Force

Introduction

When a force is applied to an object, it can cause the object to accelerate. The relationship between force, mass, and acceleration is described by Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this article, we will use this formula to calculate the net force acting on a 450 kg piano that has an acceleration of $+6.0 \, \text{m/s}^2$ .

Understanding Newton's Second Law of Motion

Newton's second law of motion is a fundamental concept in physics that describes the relationship between force, mass, and acceleration. The law is often expressed mathematically as $F = ma$ , where $F$ is the net force acting on an object, $m$ is the mass of the object, and $a$ is the acceleration of the object. This law can be applied to any object, from a small rock to a massive planet, and it is a crucial tool for understanding the behavior of objects in various situations.

Calculating the Net Force Acting on the Piano

To calculate the net force acting on the piano, we can use the formula $F = ma$ . We are given that the mass of the piano is 450 kg and its acceleration is $+6.0 \, \text{m/s}^2$ . Plugging these values into the formula, we get:

F = ma = (450 \, \text{kg}) \times (+6.0 \, \text{m/s}^2)

Performing the Calculation

To perform the calculation, we can multiply the mass of the piano by its acceleration:

F = (450 \, \text{kg}) \times (+6.0 \, \text{m/s}^2) = 2700 \, \text{N}

Interpreting the Result

The result of the calculation is a net force of 2700 N acting on the piano. This means that the piano is experiencing a force of 2700 N in the positive direction, which is causing it to accelerate at a rate of $+6.0 \, \text{m/s}^2$ .

Understanding the Direction of the Force

The direction of the force is indicated by the plus sign (+) in the result. This means that the force is acting in the same direction as the acceleration, which is in the positive direction.

Conclusion

In conclusion, we have used Newton's second law of motion to calculate the net force acting on a 450 kg piano that has an acceleration of $+6.0 \, \text{m/s}^2$ . The result of the calculation is a net force of 2700 N acting on the piano in the positive direction.

Frequently Asked Questions

What is Newton's second law of motion? Newton's second law of motion is a fundamental concept in physics that describes the relationship between force, mass, and acceleration. The law is often expressed mathematically as $F = ma$ , where $F$ is the net force acting on an object, $m$ is the mass of the object, and $a$ is the acceleration of the object.
How do I calculate the net force acting on an object? To calculate the net force acting on an object, you can use the formula $F = ma$ , where $F$ is the net force acting on the object, $m$ is the mass of the object, and $a$ is the acceleration of the object.
What is the direction of the force acting on the piano? The direction of the force acting on the piano is in the positive direction, which is the same direction as the acceleration.