A server at a diner slides a 0.521 kg root beer from the end of the counter to a thirsty customer. A force of friction of 1.32 N brings the drink to a stop right in front of the customer. What is the coefficient of kinetic friction between the glass and the counter?
F(fr)=μ•N=μ•m•g
μ=F(fr)/mg
To find the coefficient of kinetic friction, we'll need to use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
In this case, the net force is the force of friction, and the acceleration is the unknown. We know the mass of the root beer is 0.521 kg, and the force of friction is 1.32 N. The formula we'll use is:
Force (friction) = mass × acceleration
Now, rearranging the formula to solve for acceleration:
acceleration = Force (friction) / mass
Plugging in the given values:
acceleration = 1.32 N / 0.521 kg
Now we have the acceleration. Next, we'll use the equation for kinetic friction:
Force (friction) = coefficient of kinetic friction × normal force
The normal force is the force exerted by the counter on the root beer. Since the root beer is not moving up or down, the normal force is equal to the weight of the root beer (mg), where m is the mass and g is the acceleration due to gravity (9.8 m/s^2).
normal force = mass × acceleration due to gravity
normal force = 0.521 kg × 9.8 m/s^2
Now we can substitute the values into the equation for kinetic friction:
1.32 N = coefficient of kinetic friction × (0.521 kg × 9.8 m/s^2)
Simplifying:
1.32 N = coefficient of kinetic friction × 5.102 N
Solving for the coefficient of kinetic friction:
coefficient of kinetic friction = 1.32 N / 5.102 N
coefficient of kinetic friction ≈ 0.258
Therefore, the coefficient of kinetic friction between the glass and the counter is approximately 0.258.