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$\bullet$$\bullet$ The coefficients of static and kinetic friction between a476 $\mathrm{N}$ crate and the warehouse floor are 0.615 and 0.420 ,respectively. A worker gradually increases his horizontal pushagainst this crate until it just begins to move and from then onmaintains that same maximum push. What is the accelerationof the crate after it has begun to move? Start with a free-bodydiagram of the crate.

1.9 $\mathrm{m} / \mathrm{s}^{2}$

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

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Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:49

The coefficients of static…

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A 50.0 kg crate rests on t…

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A large crate is at rest o…

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The coefficient of kinetic…

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A worker pushes horizontal…

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A worker wants to turn ove…

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04:27

A dockworker loading crate…

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05:40

A worker pushes horizonta…

03:44

A $136-\mathrm{kg}$ crate …

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02:35

Two workers are sliding a …

05:56

The coefficient of static …

All right, So they're free Body diagram for this situation is given. Here you have, ah, force of gravity acting downwards. You have normal for us acting directly opposite that. And you have 47 applied Force, which we're calling Jeff That is pushing, pushing the curtain too. Right? And there is a fictional forrest obviously opposing that motion acting to the left. Okay, so we solved this by applying Newton's second law. And let's start with the wide affection. Ah, and in the white direction, we have no net force. So what we have is an equals w normal force equals, um the weight and were given that weight is for 76 Newtons. Ah, by the way, let's do him. Let's find mass for this crate because we don't know the mass were given weight and w is empty. So mass will be wait over G. How about before 76 names over 9.8 meters per second squared and this is Justin. This is for 48.6 kilograms. So? So then we Then we raise our forces in the ex direction. It's amazing. X on dh. There is motion in the extra action. There is an ex salvation. So the nautical zero this gives us though is that f minus? That's a care friction force is equal to m times the ex elevation. And if we are after something we have to find So same for can s o it's actually find those two f is equal tio new sub Ah, Mrs s Times And that's the maximum force for static from static friction s So this is just music mass times and it's w so of so that would be a 0.3. What would be our? What's point 615? That be 0.615 The times the wait for 76 And so the Applied Force F is just 293 news, right? And then the fictional force that cares a different profession miss of care times the same day on the force. And so that's point 30 r. Point for two times for 76. And I guess it's 200 Newtons and therefore ex ace of X is the difference between the two books is the difference between the two divided by mass and so that would be 2 93 minus 200 Newtons over 46 kilograms and so we get acceleration off 1.91 meters per second squared and that's it.

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