Concept explainers
The forces
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Precalculus
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- Find the work done by the force F = 2i - 7j in moving an object from the point (2, 1) to the point (9, -16). W =arrow_forwardA force field is given by the equation. A particle is moved from (1,0,0) to (1,1,1) along a straight line. Calculate the work done by the force field on the particle.arrow_forwardThe line of action of the 2690-lb force runs through the points A and B as shown in the figure. Determine the x and y scalar components of F. Answers: Fx= Fy A (-10,-4) || i i y, m 1 1 Ox B (8, 7) F = 2690 lb -x, m lb lbarrow_forward
- In the system shown, m = 4 kg, 0 = 40°, µ¸ = 0.5 and µk = 0.3 and the wheels are frictionless. (a) Determine the maximum value of force P for the system to have static equilibrium. Call this force Pmax (Pmax = 105.7 N) (b) Determine the force P for the system to have dynamic equilibrium, that is, moves with constant velocity, while moving up the incline. (P = 93.7 N) = 2Pmax, determine the accel- (c) If the system is released from rest with the cable taught and P eration of the bodies and the tension of the cable. (a = 9.81 m/s², T = 147 N) μς, μκ < 2m Ꮎ m Parrow_forwardAnswer detailly 6arrow_forward(14) The straight line L passes through the origin O and is in the direction i+mj. The straight line L' passes through the point A whose position vector is ai and is in the direction i+m'j. Write down the vector equations of L and L' and find the position vector of their point of intersection.arrow_forward
- 1. State whether the following are scalar or vector quantities: (a) A temperature of 50 °C (b) A downward force of 80N (c) 300J of work (d) A south-westerly wind of 15 knots (e) 70m distance (f) An acceleration of 25m/s2 at 30 to the horizontalarrow_forwardSuppose that over a certain region of space the electrical potential V is given by the following equation. V(х, у, 2) %3 4x2 - Зху + хуz (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i +j- k. (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P?arrow_forwardAn ant walks due east at a constant speed of 2 mi/hr on a sheet of paper that rests on a table. Suddenly, the sheet of paper starts moving due southeast at v2 mi/hr. The following is a correct solution for finding the resultant speed and direction of the ant relative to the table. Set up a coordinate system so that the positive y-axis corresponds to north and the positive x-axis corresponds to east. Then the velocity vector for the ant relative to the paper is given by (2,0). The velocity vector for the paper relative to the table is given by (v2 cos (-4), v2 sin (-5))= (1, –1). Therefore, the resultant velocity vector is given by (2,0) + (1, –1) = (3, –1). The speed of the ant relative to the table is v32 + 1² = v10 mi/hr and the direction the ant is traveling relative to the table is found by (금) using tan 0 = -1 where 0 represents the angle made with the positive r-axis. In this case 0 = arctan 3 3arrow_forward
- LA rigid body is acted on by two forces, F =ai + bj - k at the point (1,2,-1) and F =i+aj +bkat the point (-1, 0,1). If the force systemis equipollent to the force F and the couple G, which have no components along k, then determine F.arrow_forwardB4-BCT35: Box ATTACHED TO SPRING-ENERGY BAR CHART A 40-N box is initially at rest on a smooth (frictionless) horizontal surface. An unstretched spring with spring constant 10 N/m connects the box to the wall. A 60 N force is applied horizontally to the right. Complete the energy bar chart for the spring-block-earth system as the block moves a distance of 2 m. Label the column heights. Set the zero point for the gravitational potential energy at the center of the block. 60 N W 40 N Initial system energy During Final system energy KE PE PE KE PE PE eat Bar chart key KE Kinetic energy Gravitational PE potential energy Spring ptpotential energy Work done by e external forcés Use g= 10 m/s for simplicity O PE W. Explain your reasoning.arrow_forward(7) The effect of a slam dunk can be simulated by a force F = 47 lb acting at the front edge of the rim at point A shown. Use the scalar components approach to determine the moments of the force F about point O Mo and point B MB. Ans: Mo=81.5 lb-ft CCW, MB = 115.9 lb-ft CW -36"- B 12" 28" 10' Farrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage