A 20 kg bag of luggage is rolled across a horizontal floor by a force of 50 N applied to the handle which makes an angle of 65 degrees with the horizontal. If the bag moves at constant speed, what is the coefficient of friction between the bag and the floor?
It is not clear to me if the force is pushing or pulling the bag. It makes a big difference.
To find the coefficient of friction between the bag and the floor, we need to consider the forces acting on the bag. In this case, there are two main forces at play:
1. The force applied to the bag handle, which we'll call F_applied.
2. The force of friction between the bag and the floor, which we'll call F_friction.
First, let's resolve the applied force into its horizontal and vertical components. The horizontal component of the applied force is given by F_applied_horizontal = F_applied * cos(θ), where θ is the angle between the applied force and the horizontal. Similarly, the vertical component of the applied force is given by F_applied_vertical = F_applied * sin(θ).
Since the bag is moving at constant speed, we know that the net force acting on it is zero. This means that the horizontal component of the applied force must be equal in magnitude and opposite in direction to the force of friction. In equation form: F_applied_horizontal = F_friction.
Given that F_applied = 50 N and θ = 65 degrees, we can calculate the horizontal component of the applied force: F_applied_horizontal = 50 N * cos(65 degrees).
Now, we can equate the horizontal component of the applied force to the force of friction: F_applied_horizontal = F_friction. Rearranging this equation, we get: F_friction = F_applied_horizontal.
Finally, we can calculate the coefficient of friction using the equation: F_friction = coefficient of friction * normal force. In this case, the normal force is equal to the weight of the bag, which is given by weight = mass * gravity.
Putting it all together, here are the steps to find the coefficient of friction:
1. Calculate the horizontal component of the applied force: F_applied_horizontal = F_applied * cos(θ).
2. Equate the horizontal component of the applied force to the force of friction: F_applied_horizontal = F_friction.
3. Calculate the weight of the bag: weight = mass * gravity.
4. Solve for the coefficient of friction using the equation: F_friction = coefficient of friction * weight.
Note: The value of gravity can be assumed to be 9.8 m/s^2.
Let's calculate the coefficient of friction: