Bonnie and Clyde are sliding 500 bank safe across the floor to their getaway car. The safe slides with a constant speed if Clyde pushes from behind with 385 of force while Bonnie pulls forward on a rope with 300 of force.What is the safe's coefficient of kinetic friction on the bank floor?
Excellent if clearly mention the given data and free body daigram give more weightage thank you
Well, Bonnie and Clyde seem to be quite the dynamic duo! Now, let's solve this puzzling safe-sliding situation.
To find the coefficient of kinetic friction, we first need to determine the net force acting on the safe. The net force is the difference between the force applied by Bonnie and the force applied by Clyde.
The force applied by Bonnie is 300 N, while Clyde's force is 385 N. So, the net force is 385 N - 300 N, which gives us 85 N.
The coefficient of kinetic friction (μ) can be calculated using the formula:
μ = Net Force / Normal Force
Since the safe is sliding at a constant speed, the normal force is equal to its weight, which we can calculate as:
Weight = mass * gravity
Now, assuming the mass of the safe is 500 kg and the acceleration due to gravity is 9.8 m/s², we can determine the weight:
Weight = 500 kg * 9.8 m/s²
After calculating the weight, we'll use it to calculate the coefficient of kinetic friction using the net force:
μ = 85 N / (500 kg * 9.8 m/s²)
Let me grab my calculator... and ta-da! The coefficient of kinetic friction on the bank floor for the safe is approximately 0.017. So, it seems like the safe is having a bit of a slippery time getting away!
To calculate the coefficient of kinetic friction, we need to use the forces applied by Bonnie, Clyde, and the weight of the safe.
First, let's find the net force acting on the safe. Since the safe is moving with a constant speed, we know that the net force is equal to zero.
Net force = 0
The net force is equal to the sum of all the forces acting on the safe. In this case, there are two forces:
1. The force applied by Clyde pushing from behind: 385 N
2. The force applied by Bonnie pulling forward on the rope: 300 N
Since they have opposite directions, we need to consider their signs. Let's assume that the force applied by Bonnie is positive and the force applied by Clyde is negative.
Net force = Force applied by Bonnie - Force applied by Clyde
0 = 300 N - (-385 N)
0 = 300 N + 385 N
0 = 685 N
Now, let's consider the force of kinetic friction. The force of kinetic friction can be calculated using the equation:
Force of kinetic friction = coefficient of kinetic friction * Normal force
The normal force is equal to the weight of the safe, which can be calculated using the equation:
Weight = mass * gravity
Assuming the weight of the safe is W and the coefficient of kinetic friction is μ:
Force of kinetic friction = μ * W
Since the net force is zero, the force of kinetic friction must be equal to the sum of the forces applied by Bonnie and Clyde:
Force of kinetic friction = 300 N + (-385 N)
Force of kinetic friction = -85 N
Now we can substitute this value into the equation to find the coefficient of kinetic friction:
-85 N = μ * W
To find the weight of the safe, we need to know its mass. Let's assume the mass of the safe is m:
Weight = m * gravity
Since the acceleration due to gravity is constant at approximately 9.8 m/s^2:
Weight = m * 9.8 m/s^2
We can rearrange this equation to solve for the mass:
m = Weight / 9.8 m/s^2
Since the weight is equal to the force applied by Clyde (-385 N), we can substitute it in:
m = (-385 N) / 9.8 m/s^2
Now we have enough information to calculate the coefficient of kinetic friction:
-85 N = μ * (m * 9.8 m/s^2)
Solving for μ:
μ = -85 N / (m * 9.8 m/s^2)
Substitute the mass value we obtained:
μ = -85 N / (m / 9.8 m/s^2 * 9.8 m/s^2)
Simplifying:
μ = -85 N / m
Since we don't have the specific mass of the safe, we cannot determine the exact value of the coefficient of kinetic friction.
Ws = 500kg * 9.8N/kg = 4900 N. = Wt. of safe.
Fv = 4900 N. = Force perpendicular to floor.
Fk = u*Fv = u*4900 = Force of kinetic friction.
Fn = Fap - Fk = m*a
(385+300) - 490u = m*0 = 0
685 - 4900u = 0
-4900u = -685
u = 0.140.