A 5-kg box is pushed across a horizontal floor by a 20-N force that is angled 30 degrees
below the horizontal. What is the coefficient of kinetic friction between the box and the floor if
the box is pushed at a constant speed?
ma=Fcosα-F(fr)
ma=0
F(fr) = μmg
Fcosα= μmg
μ=Fcosα/mg =
=20•cos30/5•9.8=0.35
To find the coefficient of kinetic friction between the box and the floor, we need to consider the forces acting on the box.
First, let's break down the 20-N force into its horizontal and vertical components. The horizontal component can be found using trigonometry:
Horizontal component = Force * cos(angle)
= 20 N * cos(30°) ≈ 17.32 N
Next, we need to determine the force of kinetic friction acting on the box. Since the box is moving at a constant speed, the force of kinetic friction must be equal in magnitude and opposite in direction to the horizontal component of the applied force.
Force of kinetic friction = - Horizontal component
= - 17.32 N
Now, we can calculate the coefficient of kinetic friction using the equation:
Force of kinetic friction = coefficient of kinetic friction * Normal force
Since the box is on a horizontal floor and is not accelerating vertically, the normal force acting on the box is equal to its weight:
Normal force = mass * gravitational acceleration
= 5 kg * 9.8 m/s^2
= 49 N
Substituting the values, we have:
-17.32 N = coefficient of kinetic friction * 49 N
Simplifying, we find:
coefficient of kinetic friction ≈ -17.32 N / 49 N
≈ -0.353
Since the coefficient of friction cannot be negative, we take the absolute value of the result:
coefficient of kinetic friction ≈ 0.353
Therefore, the coefficient of kinetic friction between the box and the floor is approximately 0.353.
To find the coefficient of kinetic friction between the box and the floor, we need to analyze the forces acting on the box.
1. The applied force has a magnitude of 20 N and is angled 30 degrees below the horizontal.
2. The weight of the box, which acts straight downward, can be calculated using the formula:
Weight = mass x acceleration due to gravity.
Since the mass of the box is 5 kg and the acceleration due to gravity is approximately 9.8 m/s^2,
Weight = 5 kg x 9.8 m/s^2 = 49 N.
3. The normal force, which is exerted by the surface and acts perpendicular to the surface, cancels out the vertical component of the applied force. It can be calculated as the weight of the box minus the vertical component of the applied force.
Normal Force = Weight - Vertical Component of Applied Force
Normal Force = 49 N - (20 N * sin 30)
Normal Force = 49 N - (20 N * 0.5)
Normal Force = 49 N - 10 N
Normal Force = 39 N.
Now, we can calculate the force of friction using the equation:
Force of Friction = Coefficient of Kinetic Friction x Normal Force.
Since the box is moving at a constant speed, the applied force must equal the force of friction.
Therefore, 20 N = Coefficient of Kinetic Friction x 39 N.
To find the coefficient of kinetic friction, we can rearrange the equation:
Coefficient of Kinetic Friction = 20 N / 39 N.
Coefficient of Kinetic Friction ≈ 0.513.
Therefore, the coefficient of kinetic friction between the box and the floor is approximately 0.513.