A 50-kg cart is on an incline of 30 degrees above the horizontal. The cart is at rest. The static coefficient of the slope is 0.85 and the kinetic coefficient is 0.50. What is the force due to friction on the cart?

Answers

Answer 1

The cart is at rest, so it is in equilibrium and there is no net force acting on it. The only forces acting on the cart are its weight (magnitude w), the normal force (mag. n), and the friction force (maximum mag. f ).

In the horizontal direction, we have

n cos(120º) + f cos(30º) = 0

-1/2 n + √3/2 f = 0

n = √3 f

and in the vertical,

n sin(120º) + f sin(30º) + (-w) = 0

n sin(120º) + f sin(30º) = (50 kg) (9.80 m/s²)

√3/2 n + 1/2 f = 490 N

Substitute n = √3 f and solve for f :

√3/2 (√3 f ) + 1/2 f = 490 N

2 f = 490 N

f = 245 N

(pointed up the incline)


Related Questions

Other Questions
What is (1 +i)5?-4-4i-4+4i4-4i4+4i According to reports, what did Mansa Musa have built every Friday on his hajj? aAll of the choices bA mosque cA palace dA school Which of the following is the BEST definition for e-commerce? *buying items using credit cards instead of cashbuying and selling items electronically on the internetusing computers as part of the process of buying and selling itemsbuying and selling items on Amazon Id like to leave my extra cash to Debbie Cathi and lisa( 5 errors ) In the right triangle below, an altitude is drawn to the hypotenuse. Solvefor x. Given a quadratic function that is reflected across the1X-axis, vertically compressed by a factor of shifted33 units to the right, and 2 units down, write the equationof this quadratic function in vertex form. HURRY! ILL GIVE BRAINLIEST TO FIRST PERSON TO ANWSER.Which of the following statements best describes the plants and animals found in the desert regions in the Middle East?A.They have adapted to harsh climate conditions.B.They have failed to adapt to recent droughts.C.They have been unable to survive high soil salinity.D.They have always migrated toward areas with more rainfall. Suppose 56V% of politicians are lawyers. If a random sample of size 787787 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by greater than 4%4% The graph shows the relationship between time a machine soda can make. Use the points (5,240) and (8,384) to find the number of soda bottles the machine can make each minute The machine can make (???) soda bottles each minute PLS NEED HELP! THIS IS DUE IN 10MIN!!!!In trapezoid ABCD, points M and N are arbitrary points on bases AB and CD respectively. Find the area of the trapezoid, if area A ABM =23 cm and area A CMD =18 cm . Find the area of the trapezoid The equation [tex]\frac{24x2+25x-47ax}{-2=8x-3-53}[/tex]ax2 is true for all values of x2/a, where a is a constant.What is the value of a?A) -16B) -3C) 3D) 16 Around 240 million years ago, large reptiles called nothosaurs ruled the seas. These now-extinct sea monsters grew roughly five meters long or longer and flicked their long tails to speed through the water, chasing down fish.Now researchers have found fossils of a type of mini nothosaur with features that suggest the creature lived a very different lifestyle from its bigger cousins. Brevicaudosaurus jiyangshanensis may have lurked on the shallow seafloor, floating motionless until unsuspecting prey got too close, say researchers, who describe the new species October 28 in the Journal of Vertebrate Paleontology.Two B. jiyangshanensis fossils were found in quarries about a kilometer apart in South China. Their size just about a half meter long, or about the size of a beagle made the team initially think that it had stumbled upon baby nothosaurs, says Xiao-Chun Wu, a paleobiologist at the Canadian Museum of Nature in Ottawa.Two Brevicaudosaurus jiyangshanensis fossils.Two Brevicaudosaurus jiyangshanensis fossils (shown) that are roughly 55 centimeters long were discovered in South China.But the bones told a different story. In the young [nothosaurs], the bones especially in the limbs are roundish, Wu says. However, the bones in these fossils were developed into well-defined shapes, and the skull bones on the side of the head were fused, evidence that the creatures were adults. B. jiyangshanensis had various features not found on bigger nothosaurs. Its tail was short, broad and flat, and its bones were dense, all of which could have helped the reptile balance its body as it floated in shallow water.This is the first discovery of a small-sized species of a big-sized group, Wu says. This is a very new lifestyle we now know about nothosaurs.The newly described reptile may have had large lungs relative to its body size, compared with other nothosaurs, helping it to stay underwater for longer. But future skeletal studies are needed to confirm that. Whats the point of the article: What did you find interesting about the article: How does the article connect to science: Which elements are part of Roosevelt's delivery style? Check all that apply.1formal language2medium volume3emotional expression4steady pace5quick pace1,2,&4 are the answers Solve for the missing variables.x= ?y= ? Making sure that data collected on customer trends is organized is one way technology can help a business.TrueFalse Can Someone help me with this Question? Write the equation for a line that passes through (5,-4) and is perpendicular to thelinear function 2x - 10y = 0 Add or subtract as indicated.(3 + 3i) - (3 + 2i) + (1 + 41) What is the purpose of the European Union? A.to enforce global peace treaties through military interventionB.to maintain the largest standing army in the world as a deterrentC.to promote peace, security, and justice through cooperationD.to create a single, federal state covering the European continent 2 Dillards writing style in the essay serves to