a 10-g fridge magnet is holding a 2.0 piece of paper on the stainless steel fridge door. A normal force of 0.19 N( the horizontal force of the fridge pushing against the attractive, horizontal, magnet accelerated down the fridge with a net acceleration of 0.150 m/s2 when the fridge door is slammed. What is the coefficient of kinetic friction between the steel door and paper?
To find the coefficient of kinetic friction between the steel door and paper, we can use the concept of Newton's second law and apply it to the forces acting on the system. The equation for the net force acting on an object is given by:
net force = mass * acceleration
In this case, the net force is the horizontal force of the fridge pushing against the magnet, which causes the paper to accelerate. The mass of the paper is given as 2.0 grams, but we need to convert it to kilograms:
mass = 2.0 g = 0.0020 kg
The acceleration is given as 0.150 m/s^2, and we want to find the coefficient of kinetic friction (μ) between the steel door and the paper.
Now, let's calculate the net force. The net force acting on the paper is the difference between the force applied by the fridge magnet and the force of friction:
net force = applied force - force of friction
Since the only horizontal force acting on the system is the normal force exerted by the fridge (0.19 N), we can rewrite the equation as:
0.19 N - force of friction = (0.0020 kg) * (0.150 m/s^2)
Now, let's analyze the forces involved. The normal force and the force of friction are related by the equation:
force of friction = coefficient of friction * normal force
Substituting this relationship into the previous equation, we get:
0.19 N - (coefficient of friction) * (0.19 N) = (0.0020 kg) * (0.150 m/s^2)
Simplifying the equation:
0.19 N - (coefficient of friction) * (0.19 N) = 0.0003 N
Rearranging the equation to isolate the coefficient of friction:
(coefficient of friction) * (0.19 N) = 0.19 N - 0.0003 N
(coefficient of friction) * (0.19 N) = 0.1897 N
(coefficient of friction) = 0.1897 N / 0.19 N
Finally, we find:
(coefficient of kinetic friction) ≈ 0.998
Therefore, the coefficient of kinetic friction between the steel door and the paper is approximately 0.998.
To find the coefficient of kinetic friction between the steel door and paper, we can use the following steps:
Step 1: Identify the forces acting on the paper.
In this case, the forces acting on the paper are:
- Weight (mg), where m represents the mass of the paper and g is the acceleration due to gravity.
- Normal force (N) exerted by the magnet and the fridge door.
Step 2: Calculate the weight of the paper.
Since the weight is given by the formula W = mg, we can calculate the weight of the paper using the given information. However, we need the mass of the paper first. Unfortunately, it is not provided. Please provide the mass of the paper in grams or kilograms.
Once the mass of the paper is provided, we can calculate the weight.
Step 3: Calculate the net horizontal force acting on the paper.
Since the paper is accelerating down the fridge with a net acceleration of 0.150 m/s^2, it means that the net horizontal force acting on the paper is given by the formula F_net = ma, where m is the mass of the paper and a is the acceleration. We can use this information to calculate the net horizontal force.
Step 4: Calculate the frictional force.
The frictional force is given by the formula F_friction = μN, where μ is the coefficient of kinetic friction and N is the normal force.
Step 5: Solve for the coefficient of kinetic friction.
Since we already know the net horizontal force and the normal force, we can substitute these values into the formula for the frictional force and solve for the coefficient of kinetic friction.
Please provide the mass of the paper so that we can proceed with the calculations.