Calculating the Force Required to Accelerate a 90 kg Bike to 20 m/s in 15 Seconds

Understanding the physics involved in accelerating a bike can be fascinating and useful for both educational and practical scenarios, such as car engineering or sports. In this article, we explore how to calculate the force required to accelerate a 90 kg bike to a velocity of 20 meters per second (m/s) within 15 seconds.

Introduction to Momentum and Force

To comprehend the calculation of force in this scenario, it is essential to revisit the fundamental principles of momentum and force. Momentum (p) is defined as the product of an object's mass (m) and its velocity (v), expressed as p mv. Force (F) is the rate of change of momentum over time, which can be mathematically represented as:

[ F frac{Delta p}{Delta t} ]

Where ( Delta p ) represents the change in momentum and ( Delta t ) is the time interval over which this change occurs.

Initial Momentum Calculation

Given that the bike starts from rest, its initial momentum is zero. The final momentum can be calculated as follows:

[ p_{final} m times v_{final} ]

Substituting the given values:

[ p_{final} 90 , text{kg} times 20 , text{m/s} 1800 , text{kg m/s} ]

Now that we know the final momentum, we can proceed to calculate the force by determining the change in momentum and the time over which this change occurs.

Calculating the Force

The change in momentum is simply the final momentum since the initial momentum is zero. Thus, the force (F) can be determined using the formula:

[ F frac{Delta p}{Delta t} ]

Simplifying this, we get:

[ F frac{1800 , text{kg m/s}}{15 , text{s}} 120 , text{N} ]

Therefore, the force required to accelerate the 90 kg bike to 20 m/s in 15 seconds is 120 Newtons.

Application of Newton's Second Law

This calculation is a practical application of Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be expressed as:

[ F m times a ]

Where ( m ) is the mass of the object and ( a ) is its acceleration.

To find the acceleration (a) involved in this scenario, we use the formula for acceleration:

[ a frac{Delta v}{Delta t} ]

Substituting the values:

[ a frac{20 , text{m/s} - 0 , text{m/s}}{15 , text{s}} frac{20 , text{m/s}}{15 , text{s}} frac{4}{3} , text{m/s}^2 approx 1.33 , text{m/s}^2 ]

Using the mass (m 90 kg), we can verify the force through Newton's second law:

[ F 90 , text{kg} times 1.33 , text{m/s}^2 120 , text{N} ]

Conclusion

Understanding the principles of momentum and force is crucial for any application involving acceleration. This article has provided a detailed step-by-step guide to calculating the force required to accelerate a 90 kg bike to 20 m/s in 15 seconds, using both the rate of change of momentum and Newton's second law. These principles have wide-ranging applications in physics, engineering, and everyday scenarios.

For further reading, explore more about momentum, force, and Newton's laws, which form the basis of classical mechanics.