A crate of 45.0 -kg tools rests on a horizontal floor. You...

A crate of 45.0 -kg tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it and observe that the crate just begins to move when your force exceeds 313 $\mathrm{N}$ . After that you must reduce your push to 208 $\mathrm{N}$ to keep it moving at a steady 25.0 $\mathrm{cm} / \mathrm{s}$ , (a) What are the coefficients of static and kinetic friction between the crate and the floor? (b) What push must you exert to give it an acceleration of 1.10 $\mathrm{m} / \mathrm{s}^{2} ?$ (c) Suppose you were performing the same experiment on this crate but were doing it on the moon instead, where the acceleration due to gravity is 1.62 $\mathrm{m} / \mathrm{s}^{2} .$ (i) What magnitude push would cause it to move? (ii) What would its acceleration be if you maintained the push in part (b)?

Key Concepts

Static Friction

Static friction is the force that must be overcome to initiate the relative motion between two surfaces in contact. It acts up to a maximum value, which is proportional to the normal force through the coefficient of static friction. This concept is key in determining the threshold force needed to start moving an object from rest.

Kinetic Friction

Kinetic friction is the resistive force acting between surfaces in relative motion. Once an object is moving, the kinetic friction force—calculated as the product of the coefficient of kinetic friction and the normal force—usually has a lower magnitude than the maximum static friction. It is essential in analyzing the forces during constant motion or acceleration.

Normal Force

The normal force is the perpendicular contact force exerted by a surface to support the weight of an object resting on it. In friction problems, the normal force is crucial as it directly influences both static and kinetic frictional forces, typically equal to the product of mass and gravitational acceleration when the surface is horizontal.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F_net = m × a). This principle is fundamental in analyzing motion, as it relates the applied force, frictional forces, and resulting acceleration of the object.

Gravitational Acceleration

Gravitational acceleration is the acceleration due to the force of gravity acting on objects near a planetary surface. It plays a significant role in determining the weight of an object, and thereby the normal force, which in turn affects frictional forces. Changes in gravitational acceleration, such as those experienced on different celestial bodies, will alter the friction and motion dynamics.

Transcript

00:01 Okay, so we have a crate of 45 kilograms and we want to know what we know that it takes 313 newtons for this crate to start moving and once that it's moving it takes 208 nons to keep it moving okay and we want to find the coefficients the friction coefficients and we want to know what force do we do we we need to have the acceleration of 1 .1 meters per second square and basically some of the same but if we are in the moon okay so for the first part okay i'm going to write it here what it means that it takes 313 atoms to start moving okay remember that if i give it a push here with a force of 330 newtons okay remember then there is a force that is the friction force that opposes movement okay and this force what it means that i need 330 neutrons for this to start moving is that when i have 330 newtons this is actually the same as the friction of static static friction okay and this means okay that static friction is this value okay and once this means the for newton's second law the sum of of forces equals zero and once i i am a little bit let's say 313 it's the limit once i'm a little bit beyond that this thing starts moving okay so the first thing i have to calculate is the normal okay i know that the normal remember is it's the perpendicular okay goes upward and i can calculate it as the normal equals the mass times the gravity okay i know the mass is 45 kilograms and the gravity or the acceleration of gravity is 9 .8 meters per second square okay and this gives that the normal okay is 441 newtons okay now i know that the coefficient of yeah no more like the force of friction okay of static friction equals the coefficient of friction times the normal okay i want to calculate the coefficient so i rearrange and find that this is the force and friction the static friction divided by the normal i know that this and like the maximum value of the force of friction is the 330 newtons i need for to push this grade to start moving and i know the value of the normal i'll just calculate actually the units go away as this is a coefficient and i get that a 0 .71 it's the coefficient okay so the coefficient of static friction is 0 .71 this is the first answer and for the kinetic friction or the kinetic coefficient i have something like it's exactly the same formula okay i only change that it is in movement, okay? so actually i require less force, okay? and i have that this is the kinetic friction times the normal.

04:19 I know that this is 208, it's a value i'm given.

04:23 Okay, this is the force i need to keep it moving.

04:27 If i give less force, it will stop.

04:31 So, and the normal it stays the same, okay? and if you make this calculation this is 0 .472 okay so the coefficient of kinetic friction is 0 .47 okay now the second part what push or what force do i need to accelerate to 1 .1 meter per second square okay so this is the kinetic friction because i have a movement okay so i know that the force, okay, it's equal to mass times the acceleration, and this is equal to the force i give, okay, and let's say this is a total force or something like that, okay, minus the force, the friction force, okay? so remember this is in the opposite direction of this, that's the one we are playing.

05:33 So as long as this is bigger than the force of friction, this will keep moving.

05:39 Okay, that it was this limit of 208...

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