Bonnie and Clyde are sliding a 300 kg bank safe across the...

Bonnie and Clyde are sliding a $300 \mathrm{kg}$ bank safe across the floor to their getaway car. The safe slides with a constant speed if Clyde pushes from behind with $385 \mathrm{N}$ of force while Bonnie pulls forward on a rope with $350 \mathrm{N}$ of force. What is the safe's coefficient of kinetic friction on the bank floor?

Key Concepts

Normal Force

The normal force is the support force exerted by a surface perpendicular to the object in contact with it. In horizontal motion, if there are no additional vertical forces, the normal force is typically equal to the object's weight, which is essential for calculating frictional forces.

Force Equilibrium

Force equilibrium occurs when all the forces acting on an object balance each other out, resulting in a net force of zero. This concept is vital when analyzing situations where an object moves at a constant velocity, as it confirms that the driving forces and resisting forces, including friction, are equal in magnitude.

Newton's First Law

Newton's First Law of Motion states that an object will remain at rest or move at constant velocity unless acted upon by a net external force. In problems where an object moves with constant speed, this law implies that the sum of all forces acting on the object is zero, ensuring there is no acceleration.

Kinetic Friction

Kinetic friction is the resistive force that acts between moving surfaces, opposing the direction of motion. It is characterized by the coefficient of kinetic friction multiplied by the normal force, and it plays a crucial role in determining how much force is needed to keep an object moving at a constant speed.

Transcript

00:02 So in this question, bonnie and clyde are sliding a 300 -kilogram bank safe across the floor, and we are told that the safe slides with a constant speed.

00:13 And we're told clyde pushes from behind with 385 newtons of force, while bonnie pulls forward on a rope with 350 newtons, and we're asked to find the coefficient of kinetic friction between the safe and the bank floor.

00:29 So we need to find the coefficient of kinetic friction.

00:32 Which is typically denoted as in u .k.

00:36 And in order to do that, we're going to need to find the force of kinetic friction first.

00:41 So that's what i'm going to focus on.

00:45 Now, what i would like to do initially is just draw a free body diagram depicting all of the forces that are acting on this object.

00:54 So, of course, we have the normal force from the ground.

00:57 We have the gravitational force.

01:00 We have a force from clyde pushing forward.

01:04 So i'm going to name that fc.

01:07 And we have a force from bonnie.

01:10 I'll label fb.

01:11 She is pulling forward.

01:13 So even though one is pushing and one is pulling, those forces are directed in the same direction.

01:17 And then the force of friction is acting to oppose that motion.

01:22 So it's going in the opposite direction.

01:25 So i am going to be using this direction to the right as my positive direction.

01:29 And what i'd like to do is analyze the x direction in hopes of finding fk.

01:38 So fnet x is going to equal m -a -x.

01:45 And we're told that the box is moving at a constant speed.

01:49 So that implies that our acceleration will be equal to zero.

01:52 So i can just set the right -hand side here equal to zero.

01:55 And on the left -hand side, i'm going to add up all of the forces.

01:59 So fc plus fb minus fk.

02:03 Those are all of the forces in the x direction.

02:06 And i put a negative sign out in front of fk because it is pointing to the left.

02:11 It is pointing in the negative x direction.

02:13 Since i have fc and fb, i can just go ahead and solve for what fk is here.

02:19 So i'm going to pull fk over to the left hand side or right hand side...

Please give Ace some feedback