What Force Must Be Exerted On A Mass Of 60 Kg To Give It An Acceleration Of $10 \, \text{ms}^{-2}$ Vertically Upwards?

Introduction

In physics, the force required to accelerate an object is a fundamental concept that is often used in various real-world applications. When it comes to moving an object from rest to a certain velocity, or changing its direction, a force must be applied to it. The force required to accelerate an object depends on its mass and the desired acceleration. In this article, we will discuss the force required to accelerate a mass of 60 kg to a certain acceleration of $10 , \text{ms}^{-2}$ vertically upwards.

Understanding the Concept of Force and Acceleration

Force and acceleration are two fundamental concepts in physics that are closely related. According to Newton's second law of motion, the force applied to an object is equal to its mass multiplied by its acceleration. Mathematically, this can be expressed as:

$$F = ma$$

where $F$ is the force applied to the object, $m$ is its mass, and $a$ is its acceleration.

Calculating the Force Required

To calculate the force required to accelerate a mass of 60 kg to a certain acceleration of $10 , \text{ms}^{-2}$ vertically upwards, we can use the formula:

$$F = ma$$

Substituting the given values, we get:

$$F = 60 \, \text{kg} \times 10 \, \text{ms}^{-2}$$

$$F = 600 \, \text{N}$$

Therefore, the force required to accelerate a mass of 60 kg to a certain acceleration of $10 , \text{ms}^{-2}$ vertically upwards is 600 N.

Factors Affecting the Force Required

There are several factors that can affect the force required to accelerate an object. These include:

• Mass of the object: The more massive the object, the greater the force required to accelerate it.
• Desired acceleration: The greater the desired acceleration, the greater the force required to achieve it.
• Direction of acceleration: The direction of acceleration can also affect the force required. In this case, we are accelerating the object vertically upwards, which requires a greater force than accelerating it horizontally.
• Frictional forces: Frictional forces can also affect the force required to accelerate an object. These forces can slow down the object and require a greater force to overcome.

Real-World Applications

The concept of force and acceleration is used in various real-world applications, including:

• Rocket propulsion: The force required to accelerate a rocket to a certain velocity is a critical factor in its design and operation.
• Vehicle dynamics: The force required to accelerate a vehicle to a certain velocity is a critical factor in its design and operation.
• Sports equipment: The force required to accelerate a sports equipment, such as a tennis racket or a golf club, is a critical factor in its design and operation.

Conclusion

In conclusion, the force required to accelerate a mass of 60 kg to a certain acceleration of $10 , \text{ms}^{-2}$ vertically upwards is 600 N. This calculation is based on the formula $F = ma$, which relates the force applied to an object to its mass and acceleration. The factors that affect the force required include the mass of the object, the desired acceleration, the direction of acceleration, and frictional forces. The concept of force and acceleration is used in various real-world applications, including rocket propulsion, vehicle dynamics, and sports equipment.

Frequently Asked Questions

• What is the force required to accelerate a mass of 60 kg to a certain acceleration of $10 , \text{ms}^{-2}$ vertically upwards? The force required to accelerate a mass of 60 kg to a certain acceleration of $10 , \text{ms}^{-2}$ vertically upwards is 600 N.
• What factors affect the force required to accelerate an object? The factors that affect the force required to accelerate an object include the mass of the object, the desired acceleration, the direction of acceleration, and frictional forces.
• What are some real-world applications of the concept of force and acceleration? Some real-world applications of the concept of force and acceleration include rocket propulsion, vehicle dynamics, and sports equipment.

References

• Newton's second law of motion: This law states that the force applied to an object is equal to its mass multiplied by its acceleration.
• Formula for force: The formula for force is $F = ma$, where $F$ is the force applied to the object, $m$ is its mass, and $a$ is its acceleration.
• Real-world applications: The concept of force and acceleration is used in various real-world applications, including rocket propulsion, vehicle dynamics, and sports equipment.