Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

$\bullet$$\bullet$ A $25.0-\mathrm{kg}$ box of textbooks rests on a loading ramp thatmakes an angle $\alpha$ with the horizontal. The coefficient ofkinetic friction is $0.25,$ and the coefficient of static friction is0.35 . (a) As the angle $\alpha$ is increased, find the minimum angleat which the box starts to slip. (b) At this angle, find the accel-eration once the box has begun to move. (c) At this angle, howfast will the box be moving after it has slid 5.0 $\mathrm{m}$ along theloading ramp"?

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

(a) $\alpha=19.3^{\circ}$(b) $a_{x}=0.927 \mathrm{m} / \mathrm{s}^{2}$(c) $v_{x}=3.04 \mathrm{m} / \mathrm{s}$

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

Cornell University

University of Washington

University of Sheffield

University of Winnipeg

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.

09:43

A 25.0 -kg box of textbook…

06:22

0:00

A 25.0-kg box of textbooks…

04:23

A box with mass 10.0 kg mo…

03:03

A box with a mass of 2 $\m…

02:21

08:42

The coefficient of static …

all right question 47 states. That's a 25 kilogram box of textbooks resting loaded ramp that makes an angle. Alfa, with the horizontal coefficient of kinetic friction, is 0.25 and the coefficient of static friction. 0.35 question a state. As the angle alpha is increased, find the minimum angle at which the box starts to slip. We'll do pretty first before we move on Part eight. What is outfits such that are our weights essentially exceeds our coefficient of static friction. That's what this area we're looking at. My first label, my axes, sets that ex lives in the direction of the plane. We'll never competition is a little bit easier. So we're taking your free body diagram are making everybody dagger, I should say of our box. You know, the weight, of course, points straight downward, which means we have a why component overweight here. W why where the angle that the brand makes with the horizontal is Alfa? So if you look at the angle between these two about he's here by similar angles. This is also Alfa to the single. Here is Alfa so that our W y component would be just be the wait times. Khost, Sign Data Alfa. Sorry, this time yourself. Other angle. Which means this opposing dotted line here is W X our weight in the X direction which would be by looking at the triangle. Um w sign Alfa. So if the motion of the box would be down the ramp, that means the coefficient stack virtue. Sorry, the forces static friction would be opposing that motion. And of course, we have a normal force pointing out of the board of the line right now, I should say, looking at our forces in her extraction, you know, the forests of X has to be zero such that once it starts to move, then it starts sliding. So so you once Thea Angle is great enough, Then the book starts to slide. But until then, we're looking for the maximum ankle, which that was crap. Internet forces. Basically everybody diagram static friction force in a positive direction. Just a cataract are weak in the X direction since w sign out for equal zero, which based on that, we can clearly see that the forces that affection is something just equipment to w sign Alfa, where you replace RFs with the definition is just coefficient of static friction times of normal for us and looking at why function all right, Uh, forces, I should say that will help us find about the normal forces, which again is accelerating in the Y direction. So the net forces have to be zero as well to see the normal force point upward, which counteracts are by the weight in the Y direction that the Yukos Alfa, which equals zero, which should indicate directly that are normal forces just have the equivalent to W Coast Alvear, which I'll put back into this equation. I'm us equals w Coast It Alfa equals W Sign Alfa, which we have a weight term in both science and beautified both sides by co sign Alfa. Being us simply just equals Tan of Alfa and so we can find out if I take the inverse tangent or are kindred of us, which is 0.35 we find at this maximum angle before the books start to slide down. The ramp is 19.3 degrees party. No asked at this angle fine acceleration once the box has begun to move. So now that we're moving we look at the forces in our X direction, this has to equal and eight now. So revisiting our equations we have FS is up the ram minus r w Sign Alfa now equals and a so basically family for we know that well, now that's moving. Sorry, this is F k right? It's air Force of kinetic friction. We have U k times the normal force which you know again we found previously nothing in the y direction change So this is still valid. So you mg Coast Alfa my just w sign Alfa equals m a which may be up if I just go back a little bit. I'm replaced my weight with this to turn that and in times G as well See that I can cancel out that mass term I'm sign Alfa equals and a the master of each value so vast Cassel's own and start flipping this round being find the acceleration. It's simply new. K just 0.25 times g constant, somewhat competitive. But we all know what that is. My 0.8 meters per second squared times co sine of the angle that it tells that which is 19.3 degrees, minus G times sign of 19.3 degrees, which equals 0.92 meters per second square. What really everything about looking at are forced body free body diagram feel the exhilarating down the ramp? So really, I should inserted apologies for not the fact that is amazed, negative for me. There's a negative sign here and a negative sign out front. So our final exploration is native 0.92 meters per second squared or use a 9.92 meters per second squared down the ramp. Both are equivalent in acceptable in part C. At this angle, how fast will the boss removing after five meters after traveling five days? So we know acceleration every no distance. So in your Z's cinematic relationship that our final velocity equals our initial velocity squared plus to a d. Please use the magnitude here. Is it gonna get the names? Timeless is indicative of direction, but in terms of traveling down the ramp is the indie positive value. Or you could say you travel a negative five meters if your child, because you having any native next direction so you want me exactly. Correctness narrow right you should have negative five meters here. Our initial velocity is zero because it just started to move. So you find that a velocity at the end point for five minutes is two times eight times D. The native sign from each terms will cancel out. And so plugging in our value, our values for D here, an acceleration. We find that our final velocity is simply to two significant figures 3.0 meters per second. There you go.

View More Answers From This Book

Find Another Textbook

01:51

Ao6. If two identical waves with a phase difference of 31 are added, the res…

800 kg elevator starts from rest, moves upward for 2.50 with constant accele…

03:51

Equilibrium Rotational Motion Acellus7 Ann and Bob are carrying { 18.5 k…

01:15

Equilibrium Rotational Motion Acellus27 A 2150 kg drawbridge, 8.74 m…

01:16

Rotational Dynamics Rotational Motion Acellus27 Apotter's wheel…

01:34

7 A solid ball (m = 1.40 kg; r = 0.0622 : m) rolls from rest down frictionle…

02:34

10. A toy - truck moves off the edge of table that is 1.25 m high and lands …

04:36

16. Donovan McNabb throws football with an initial velocity of 30 m/s at an …

04:09

Iriguic[Figure 9]24.A field goal kicker lines up to kick a 44 yard (…

01:07

13.A spring with spring constant 400 N/m has an uncompressed length of 0.23 …