Calculating the Force of Friction in a Lawnmower Pushing Scenario

Understanding the forces at play when pushing a lawnmower can be quite intriguing. This article delves into the calculations required to determine the force of friction based on the initial conditions provided. We will walk through the application of Newton's Second Law step by step, ensuring a clear and comprehensive explanation.

Description of the Problem

A woman is pushing a lawnmower initially at rest with a forward force of 68.7 N. The lawnmower accelerates to a speed of 1.44 m/s over a time of 3.81 seconds. The objective is to calculate the force of friction exerted on the mower, focusing solely on the magnitude of the force.

Step-by-Step Solution

Step 1: Calculate the Acceleration of the Lawnmower

According to Newton's Second Law, acceleration is given by:

a frac{Delta v}{Delta t}

Where:

Delta; v 1.44,text{m/s} - the final velocity, starting from rest Delta; t 3.81,text{s} - the time taken for the acceleration

Calculating the acceleration:

a frac{1.44,text{m/s}}{3.81,text{s}} approx 0.378,text{m/s}^2

Step 2: Calculate the Net Force Acting on the Lawnmower

Using Newton's Second Law, the net force is:

F_{text{net}} m cdot a

Where:

m 38.7,text{kg} - the mass of the lawnmower a approx 0.378,text{m/s}^2 - the acceleration

Calculating the net force:

F_{text{net}} 38.7,text{kg} times 0.378,text{m/s}^2 approx 14.63,text{N}

Step 3: Find the Force of Friction

The net force is the difference between the applied force and the frictional force:

F_{text{net}} F_{text{applied}} - F_{text{friction}}

Rearranging gives:

F_{text{friction}} F_{text{applied}} - F_{text{net}}

Substituting the known values:

F_{text{applied}} 68.7,text{N} F_{text{net}} approx 14.63,text{N}

Calculating the frictional force:

F_{text{friction}} 68.7,text{N} - 14.63,text{N} approx 54.07,text{N}

The force of friction f is equal to 54.07 newtons, which is the force acting in the opposite direction to the applied force.

Conclusion

The problem follows a clear step-by-step approach to determine the force of friction based on basic principles of physics. This type of calculation is crucial in understanding the dynamics of pushing objects and forms the basis for more complex physics problems.

Further Reading

If you're interested in further exploring physics problems and equations, consider investigating more complex scenarios involving forces and motion. Understanding these concepts can provide valuable insights into the world of mechanics and engineering.

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