A particle moving in the xy-plane is subject to a force F(x, y) = (50 N/m)(xỉ + î) where x and y are in meters. Calculate the work done on the particle by this force, as it moves in a straight line from the point (3 m, 4 m) to the point (6 m, 8 m).
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- A particle is moved along the x-axis by a force that measures 8/(1 + x)2 pounds at a point x feet from the origin. Find the work W done in moving the particle from the origin to a distance of 7 ft.A particle moves in the xy plane (see the figure below) from the origin to a point having coordinates x = 7.00 m and y = 4.00 m under the influence of a force given by 7 = -2y²1 - 3x1. y (m) 2 (7.00, 4.00) x (m) (a) What is the work done on the particle by the force F if it moves along path 1 (shown in red)? -84 (b) What is the work done on the particle by the force F if it moves along path 2 (shown in blue)? -224 (c) What is the work done on the particle by the force F if it moves along path 3 (shown in green)? -32.7 X Your response differs from the correct answer by more than 10%. Double check your calculations. J (d) Is the force conservative or nonconservative? conservative nonconservativeA particle moves along a curved path y(x) = (10 m){1+cos[(0.1 m−1)x]} , from x = 0 to x = 10π m, subject to a tangential force of variable magnitude F(x) = (10 N)sin[(0.1 m−1)x]. How much work does the force do? (Hint: Consult a table of integrals or use a numerical integration program.)
- The force F(x,y) = [(2.56 N/m)y]i + [(3.14 N/m)x]j acts on a particle. What is the work done, in joules, by the force if the particle moves in a straight line from Cartesian coordinate (0.00 m, 0.00 m) to (4.39 m, 4.39 m)?(a) A force F= (2x1 + 4yĵ), where F is in newtons and x and y are in meters, acts on an object as the object moves in the /F. F. dr done by the force on the object (in J). x-direction from the origin to x = 4.63 m. Find the work W = J (b) What If? Find the work W = (4.63 m, 4.63 m) along a straight-line path making an angle of 45.0° with the positive x-axis. J F. dr done by the force on the object (in J) if it moves from the origin to Is the work done by this force dependent on the path taken between the initial and final points? dependent independentA force acting on a particle moving in the xy plane is given by F = (2yî + x²ĵ), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x = 5.80 m and y = 5.80 m, as shown in the figure below. y (m) (x, y) x (m) (a) Calculate the work done by on the particle as it moves along the purple path (oⒸ). (b) Calculate the work done by F on the particle as it moves along the red path (0 BC) J O conservative (c) Is F conservative or nonconservative? nonconservative
- The force on a particle is described by 2x^3−6 at a point x along the x-axis. Find the work done in moving the particle from the origin to x=7.The vector v=ai+bj is parallel to the line bx−ay=c. Use this fact to find an equation for the line through P parallel to v. Then draw a sketch of the line, including v as a vector starting at the origin. P(2,1), v=−2i−j How much work does it take to slide a crate 29 m along a loading dock by pulling on it with a 220-N force at an angle of 28° from the horizontal? (Round to the nearest whole number as needed.)Given: A shopper pushes a grocery cart for a distance 21 m at constant speed on level ground, against a 37.5 N frictional force. He pushes in a direction 22.5° below the horizontal. What is the work done on the cart by friction, in joules? What is the work done on the cart by the gravitational force, in joules? What is the work done on the cart by the shopper, in joules? Find the magnitude of the force, in newtons, that the shopper exerts on the cart. What is the total work done on the cart, in joules?
- The force F = (6.82 N)i + (4.75 N)j acts on a particle as it moves along a straight line from Cartesian coordinate (0.77 m, 1.58 m) to (7.38 m, 8.37 m). What is the work done, in joules, by the force?A constant force F = 6.0 i - 2.0 jN acts on a particle that undergoes a displacement from point A at the origin to point 2 - B located at (3.0 m, 1.0 m). Find the work (in J) done by the force on the particle.An object moves in the x-y plane while acted on by the force F(x,y) = k1yi + k2xj, where k1 and k2 are constants with units of N/m. The object moves along a straight line path from Cartesian coordinate (x1, y1) to (x2, y2). Write an expression for the work done on the object by this force.