A box is given a push so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.15 and the push imparts an initial speed of 3.9 m/s?
Acceleration, a = -μg
initial velocity, v0 = 3.9 m/s
final velocity, v = 0 m/s
Using
2aS=v²-v0², where
Distance to stop, S = (v²-v0²)/(2a)
300
To determine how far the box will go, we first need to understand the forces acting on it. In this case, the main force opposing the motion of the box is the kinetic friction between the box and the floor.
The formula to calculate the frictional force, also known as the force of kinetic friction, is:
Frictional force = coefficient of kinetic friction * normal force
The normal force is the force exerted by the surface perpendicular to the box. In this case, since the box is sliding horizontally, the normal force is equal to the weight of the box, which can be calculated as:
Weight = mass * acceleration due to gravity
Once we know the frictional force, we can calculate the acceleration of the box using Newton's second law of motion:
Force = mass * acceleration
Since the box is initially at rest, the initial velocity is 0. Using the equation of motion, we can calculate the distance traveled:
Distance = (initial velocity ^ 2) / (2 * acceleration)
Let's find the solution step by step:
1. Calculate the weight of the box:
Weight = mass * acceleration due to gravity
2. Calculate the frictional force:
Frictional force = coefficient of kinetic friction * weight
3. Calculate the acceleration of the box:
Force = mass * acceleration
Frictional force = mass * acceleration
Acceleration = Frictional force / mass
4. Calculate the distance traveled:
Distance = (initial velocity ^ 2) / (2 * acceleration)
Now, let's substitute the given values into the equations and solve for the distance traveled:
Given:
Coefficient of kinetic friction (μ) = 0.15
Initial velocity (v) = 3.9 m/s
Acceleration due to gravity (g) = 9.8 m/s² (standard value)
1. Calculate the weight of the box:
Weight = mass * acceleration due to gravity
2. Calculate the frictional force:
Frictional force = coefficient of kinetic friction * weight
3. Calculate the acceleration of the box:
Acceleration = Frictional force / mass
4. Calculate the distance traveled:
Distance = (initial velocity ^ 2) / (2 * acceleration)