Brick Sliding on a Concrete Surface: Calculating Distance and Deceleration
Imagine a brick sliding across a concrete horizontal surface with an initial velocity of 6 meters per second (m/s). If the coefficient of friction between the brick and the surface is 0.4, how far will the brick travel before coming to a complete stop? This article aims to walk you through the mathematical calculations to determine the distance traveled, utilizing both the deceleration method and the kinetic energy method.
Newton’s Second Law and Deceleration
According to Newton’s second law, the force of friction acting on the brick can be described as:
Force of Friction -μmg, where μ is the coefficient of friction, m is the mass of the brick, and g is the acceleration due to gravity (approximately 9.81 m/s2). ma -μmg, providing for the deceleration a -μg.Using these equations, we can find the deceleration:
a -0.4 * 9.81 -3.924 m/s2
Since the deceleration is a constant, we can use the equations of motion to calculate the distance the brick will travel:
s v2 / (2a) (62) / (2 * 3.924) ≈ 4.59 meters
Work Done by Friction and Kinetic Energy
The work done by friction is equal to the initial kinetic energy of the brick. The work done by friction is given by the formula:
W Fd μmgd The initial kinetic energy is given by:Ek (1/2)mv2
Setting these equal and solving for the distance d gives:
μmgd (1/2)mv2
d (1/2)v2 / (μg) (1/2) * 62 / (0.4 * 9.81) ≈ 4.587 meters
Both methods yield a very similar result, confirming the consistency of the calculations.
Conclusion
Using the principles of Newton’s second law and the concepts of work and energy, we have calculated the distance that a brick will travel on a concrete surface, starting from an initial velocity of 6 m/s, with a coefficient of friction of 0.4. The results from both approaches show that the brick will travel approximately 4.59 meters before coming to a complete stop. This calculation is essential in various real-world scenarios, from designing safe flooring to understanding the motion of sliding objects.
Reference
1. Physics Classroom on Friction 2. Khan Academy on Deceleration and Kinetic Energy