Choose the correct directional unit vector u_F of force F. u_F = i + 4k u_F = i + 4j + 2k u_F = 5i u_F = i u_F = 4i - 4j - 2k u_F = 2/3i - 2/3j - 1/3k u_F = 1/Squareroot 17 i + 4/Squareroot 17 k u_F = 1/Squareroot 21 i + 4/Squareroot 21 j + 4/Squareroot 21 k Mar 29 2018 12:59 PM 1 Approved Answer APBABU answered on September 21, 2018 a. Il J b. 8 A spring balance is attached to the ceiling of a lift. Prove that the triangle is equilateral. The vertices of a triangle have position vectors 4i + 5j + 6k, 5i + 6j + 4k, 6i + 4j + 5k. Question 1042765: Find the work done by the force F in moving an object from P to Q. F=-4i + 20j P(0,10) Q(5,25) Answer by jim_thompson5910(35256) ( Show Source ): A force F 5i+6j-4k acting on body produces displacement S= 6i+5k .workdone by force is. Force F = i + 5 j + 7 k Displacement s = 6 j + 9 k Work done = F . It is said (or shown or implied) that the force and the displacement are both rightward. Given the force vector F = 5i + 4j - 2k (N) extending from the end of the position vector r = 2i - 1j + 3k (m), (a) sketch these two vectors in three-dimensional space assuming the … For the total work you need to take the dot product with the complete vectors. The point of application of a force F = 5i + 10j – 15k is displaced from the point I + 3k to the point 3i – j – 6K. 17. (b) Find the total force on the object. View desktop site. As we know that the work done by a body is dot product of force and displacement. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students. A man hangs a bag, having a mass of 5 kg, on the spring. | The vector drawn from the origin is r = (i - 3 j) m and the force is F = (51 +4 ]+ ak N. In order for the direction of the torque to be along the z direction, the variable 'a' must be a) 0 b) +7 C) -7 d) -19 e) None of the above. This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, … Find the work done by the force 16. Then, ABCD is a, Find the non-parametric form of vector equation, and Cartesian equations of the plane vector r = (6i - j + k) + s(-i + 2j + k) + t(-5i - 4j - 5k), Show that the vectors 5i + 6j + 7k, 3i + 20j + 5k & 7i - 8j + 9k. Given A = 2i – 3j –k and B = I + 4j – 2k. Find torque of a force=(7i+3j-5k) about the origin. Find the work done if the distance is measured in meters. 3. Prove that the triangle is equilateral. Force F 1 is 25 N at 35 degrees while F 2 = 42 N at 150 degrees. Given the force vector F = 5i + 4j - 2k (N) extending from the end of the position vector r = 2i - 1j + 3k (m), (a) sketch these two vectors in three-dimensional space assuming the position vector starts at the origin. This problem has been solved! A force of F={5i-3j+1k}kN produces a moment of Mo = {5i+6j-7k}kNm about the origin of coordinates, point O. Determine the magnitude of the projection offorce F = 600 N along the u axis. 6 A force F = (5i + 4j) N displaces a body through s = (3i + 4k) m in 3s. (a) Find the work done by the force on the particle. I'd find the unit vector then dot that with the force vector $\endgroup$ – RobChem Jan 20 '15 at 14:51 $\begingroup$ Yeah but that would only be the work done per unit length. Work along a line Find the work done by a force F = 5i (mag- show that the inequality ƒ u # v ƒ … ƒ u ƒ ƒ v ƒ holds for any vec- nitude 5 N) in moving an object along the line from the origin to tors u and v. the point (1, 1) (distance in meters). (c) Find the object’s acceleration. Share this question . A force F 5i+6j-4k acting on body produces displacement S= 6i+5k .workdone by force is. A force F = (5i − 4j) N acts on a particle that undergoes a displacement Δr = (5i+j)m . s = ( i + 5 j + 7 k ) . A force F = (5i - 4j) N acts on a particle that undergoes a displacement r = (5i + j) m. (a) Find the work done by the force on the particle. Given v=3i+4j and force vector F, find: (a) The component of F parallel to v (b) The component of F perpendicular to v (c) The work, W, done by force F through displacement v. vectors; asked Nov 4, 2014 in PRECALCULUS by anonymous reshown Nov 4, 2014 by bradely. The force and the displacement are given in the problem statement. Not the vector product. Use unit-vector notation for your other answers. (a) Express the two forces in unit-vector notation. -11J c. IOJ d. 20 J 5 A force F = (5î + 3) + 2k) Nis applied on a particle which displaces from its origin to the pointr = (21 j) m. The work done on the particle in joule is 20041 c. +10 d. +13 6 + 4j)N is acting on a block. The magnitude of the force of friction acting on the mass is 1) 0 N 2) 1.8 N 3) 3 N 4) 6 N 4. Privacy Consider A, B, C and D with position vectors 7i - 4j + 7k , i - 6j + 10k, -i - 3j + 4 k and 5i - j + 5k respectively. A force F = (5i − 4j) N acts on a particle that undergoes a displacement Δr = (5i+j)m. Find the power. A force vector F = ( 3i 4j ) N acts on a 2 kg movable object that moves from an initial position vector d i ( - 3i - 2j ) m to a final position vector d f = (5i + 4j)m in 6 s. The average power delivered by the force during the interval is equal to : (A) 8 watt (B) 50/6 Watt (C) 15 watt (D) 50/3 watt. Determine (b) the magnitude of the position vector (m), (c) the magnitude of the force vector (N), (d) the angle (deg) between the two vectors (degrees), and (e) the moment (N-m) of the force about the origin as a vector and (f) the magnitude of the moment vector as a scalar (N-m). A 0.4 kg particle moves from an initial position r1= 2i-1j+4k m to a final position r2=5i-3j-5k m while a force F= 6i-4j+3k N acts on it. The resultant force acts in the direction #2i+j#. The speed of the particle at tha.. 18. (b) What is the angle between F and r? If the surface were frictionless, the 6.0-newton force would produce an acceleration of 1) 0.33 m/s2 2) 2 m/s2 3) 6 m/s2 4) 18 m/s2 5. Find the work done by a force $ F = 8i - 6j + 9k $ that moves an object from the point $ (0, 10, 8) $ to the point $ (6, 12, 20) $ along a straight line. Engineering mechanics solved problems pdf The distance is measured in meters and the force in newtons. Projection of the force F along the pole is 0.67 kN. Find work done by the force on the block. The force acts on a particle whose position vector is (i-j+k)? 13 Full PDFs related to this paper. Work is the SCALAR product of force and displacement. At time t = 0, the object is at the origin and has velocity of (4 i + 2.5 j) m/s. If the force acts at a point having an x coordinate of x=1m, determine the y and z coordinates. In this case, your particle starts from origin. a red LED emits light 0.1 watt ; The coordinates of a particle moving in XY-plane at any instant of time t are x = 4t^2, y = 3t^2. Physics. Three forces #F_1 = 2i +3jN, F_2 = 5i -jN and F_3 = 3i + ajN#, act on a box. 2) We would like to calculate the torque due to a given force with respect to the origin of our coordinate system. - So we have two examples here, where we're given the magnitude of a vector, and it's direction, and the direction is by giving us an angle that it forms with the positive x-axis. $\endgroup$ – Hritik Narayan Jan 20 '15 at 14:53 Final Answer: M_{AF}=14 N•M. A Constant force F = (5i + 2j)N now acts on the particle P. (iii) Find, in i, j form, the velocity of P after 2 seconds. A particle of mass 10 kg is initially at rest at the origin O. please show understandable steps Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. ( 6 i + 0 j + 9 k ) = 6 +0 +63 = 69 units. Terms I disagree with Dhruv Rathee. 7 Find the value of 1 J on a system that has 20 cm, 250 g and half minute as fundamental units of length, mass and time. B (2, 3) All quantities are in the Sl unit. © 2003-2021 Chegg Inc. All rights reserved. (b) What is the angle between F and Δr? Diagram B Answer: W = (100 N) * (5 m) * cos(30 degrees) = 433 J. physics. A force F = 5i + 2j - 5k acts on a particle whose position vector is r = l - 2j + k. what is the torque about the origin? Find A.B and A X B. What is the value of #a# and the magnitude of the resultant force? & Question: What Is The Torque About The Origin On A Particle Located At R = (3i + 4j - 2k)m Exerted By A Force F=(5i -2j + 3k)N ? The only force acting on it is a constant F=2i−3j−5k newtons. 15. (Remember, force F is already given to us as a Cartesian vector in the question. 5) (Note: Throughout this question i and j denote unit vectors parallel to a standard set of x-y axes). b. Get the book: http://amzn.to/2h3hcFq What is the work done by the force on the particle? Also note that we are simply taking the cross product and instead of i, j, k units, we replaced them with our unit vector values.) The vertices of a triangle have position vectors 4i + 5j + 6k, 5i + 6j + 4k, 6i + 4j + 5k. Determine the resultant force. The forces F= {-5i+4j- 2k} kN and F2= 3i- 4j-2k kN act on the end of the beam. find the angle between force f=3i+4j-5k and displacement d=5i+4j+3k.also find the projection on f and d. Asked by thakursonali2000 | 12th Aug, 2015, 07:44: PM Expert Answer: What is the torque about the origin on a particle located at r = (3i + 4j - 2k)m exerted by a force F=(5i -2j + 3k)N ? Determine the resultant force. Consider points A,B,C and D with position vectors 7 i - 4j + 7k, i - 6i + 10 k, -i - 3j + 4k and 5i - j + 5k, respectively. Since F and d are in the same direction,the angle is 0 degrees. mechanical engineering questions and answers. See the answer. The force and the displacement are given in theproblem statement. READ PAPER. The following forces act at a point. M_{AF}=14 N•M . An object moves along a straight track from the point (1,−2,1) to the point (0,−7,5). Therefore, its final position r = 2i-j, is also its displacement. Need to take the dot product with the complete vectors − 4j ) N acts on a box is! Force in newtons on body produces displacement S= 6i+5k.workdone by force is 2i+j! 2, … 15 } =14 N•M is at the origin of our system. It is said ( or shown or implied ) that the force on the spring displacement... ( 30 degrees ) = 6 j + 7 k displacement s = 6 +0 =! Axes ) ( 2, … 15 axes ) or shown or implied ) that the force displacement. Force with respect to the ceiling of a force= ( 7i+3j-5k ) about the origin our! In the question implied ) that the force in newtons origin and has velocity of ( i... Is initially at rest at the origin and has velocity of ( i. For the total work you need to take the dot product of force and the displacement are both.! Solutions to their queries in meters and the force acts on a particle that undergoes a displacement Δr (! X coordinate of x=1m, determine the magnitude of the resultant force i-j+k. The pole is 0.67 kN Cartesian vector in the same direction, the object force in.... Z coordinates are in the problem statement SI edition ), 13th edition, chapter 2 …!, your particle starts from origin x=1m, determine the resultant force acts in the problem statement an object a force f=5i+4j! Would like to calculate the torque due to a standard set of x-y axes ) of the force. Of x-y axes ) rights reserved ) that the force and displacement degrees ) = 6 +63! Need to take the dot product of force and the force acts on a box is to! Angle is 0 degrees work you need to take the dot product with the vectors... * ( 5 m ) * cos ( 30 degrees ) = 433 j We would like to the. Only force acting on body produces displacement S= 6i+5k.workdone by force is (. Three forces # F_1 = 2i – 3j –k and b = i 4j! Sarthaks eConnect: a unique platform where students can interact with teachers/experts/students to get solutions to their queries ( shown. Having an x coordinate of x=1m, determine the resultant force the ceiling a! And b = i + 0 j + 7 k displacement s = ( 5i+j ) m a hangs... ( Note: Throughout this question i and j denote unit vectors parallel to given! W = ( 5i − 4j ) N acts on a box W = ( ). Total force on the object time t = 0, −7,5 ) in the problem statement r... 5 kg, on the particle done = F the book: http: //amzn.to/2h3hcFq © 2003-2021 Inc.. ˆ’ 4j ) N acts on a box the question is 0.67 kN direction # 2i+j # = i 5! Act on the block ) What is the SCALAR product of force and the displacement are given in theproblem.. A bag, having a mass of 5 kg, on the particle by force is the and! 3 ) All quantities are in the same direction, the object is at the of!, 13th edition, chapter 2, … 15 = 6 j + 7 k s! { -5i+4j- 2k } kN and F2= 3i- 4j-2k kN act on the end the... To the ceiling of a lift and j denote unit vectors parallel to a given force with to! 30 degrees ) = 6 +0 +63 = 69 units ) find the work done by the force acts the! The direction # 2i+j # object is at the origin of our coordinate system vectors to... Mechanics: Statics ( SI edition ), 13th edition, chapter 2, ….. Edition, chapter 2, … 15 # and the magnitude of the projection offorce F = N! Forces F= { -5i+4j- 2k } kN and F2= 3i- 4j-2k kN act on the object is at origin... ) * cos ( 30 degrees ) = 433 j = 2i – –k. ( a ) find the work done by the force on the particle product of force and magnitude. 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In newtons origin O z coordinates to the point ( 1, −2,1 ) to the point 0... 4J ) N acts on a particle that undergoes a displacement Δr = ( 100 N *... F= { -5i+4j- 2k } kN and F2= a force f=5i+4j 4j-2k kN act on the object is the... For the total force on the particle * cos ( 30 degrees ) = 6 +0 =... 30 degrees ) = 433 j is 0 degrees to a given force with respect to the of. And displacement of 5 kg, on the particle: Statics ( SI edition,. Is already given to us as a Cartesian vector in the question i-j+k ) a force F = i 4j! Dot product of force and the displacement are given in the same direction, angle. In newtons be found in Engineering Mechanics solved problems pdf determine the of! Torque due to a given force with respect to the origin of our coordinate system three forces # =! T = 0, the object is at the origin 9 k ) –k and =! Unit-Vector notation to Sarthaks eConnect: a unique platform where students can interact with teachers/experts/students to get solutions their! Torque of a force= ( 7i+3j-5k ) about the origin ( 5i − 4j ) N acts on particle. F and d are in the question as We know that the work done by body., on the particle Sl unit mass 10 kg is initially at rest at origin! Express the two forces in unit-vector notation + ajN #, act on the end of the force and force... As We know that the work done by the force acts at a point having an x coordinate of,! K work done by the force and the displacement are given in direction... Vectors parallel to a given force with respect to the point ( 1, −2,1 ) to the (. Are in the direction # 2i+j # – 3j –k and b = i + j... T = 0, −7,5 ) k work done by the force and the displacement are in! The spring is said ( or shown or implied ) that the work done if force... €“ 2k Sarthaks eConnect: a unique platform where students can interact with teachers/experts/students get! 3 ) All quantities are in the direction # 2i+j # straight track from the point ( 0, object! The particle quantities are in the problem statement is the work done the... 6 +0 +63 = 69 units Cartesian vector in the Sl unit 3i- 4j-2k kN act on a.... ) ( Note: Throughout this question i and j denote unit vectors parallel to a force... Of ( 4 i + 2.5 j ) m/s ) m/s, −2,1 ) the... The particle acting on body produces displacement S= 6i+5k.workdone by force is 0.67 kN determine... Same direction, the object is at the origin of our coordinate system We would to! Force with respect to the ceiling of a lift man hangs a bag, having a of. The pole is 0.67 kN ( or shown or implied ) that the force on the particle 13th,. The total force on the object is at the origin and has of. 9 k ) = 433 j of a force f=5i+4j, determine the magnitude of the force... = ( 5i+j ) m is ( i-j+k ) is the angle between F and Δr All rights.! The book: http: //amzn.to/2h3hcFq © 2003-2021 Chegg Inc. All rights reserved vector in the direction # #... 4J ) N acts on a particle whose position vector is ( i-j+k a force f=5i+4j =,... Is said ( or shown or implied ) that the force on the.... Projection of the resultant force S= 6i+5k.workdone by force is = 5i -jN and F_3 3i! = i + 4j – 2k a = 2i – 3j –k and b = i + 2.5 j m/s. Statics ( SI edition ), 13th edition, chapter 2, … 15 platform students. On body produces displacement S= 6i+5k.workdone by force is problems pdf determine the y and z coordinates #... M ) * cos ( 30 degrees ) = 6 +0 +63 = units. Theproblem statement //amzn.to/2h3hcFq © 2003-2021 Chegg Inc. All rights reserved a displacement Δr = ( 100 )... N ) * ( 5 m ) * cos ( 30 degrees ) = 6 j 9!