The potential energy function associated with a force acting on a system is U = 3xy - 8x. What is the force at point (x, y)? (Express your answer in vector form.) F = X The force is the negative of the derivative of the potential function. To determine this force, find the partial derivatives of the potential function with respect to x and y. The negatives of these results are the components of the force vector. Need Help? Read ItThis question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise The force acting on a particle varies as shown in the figure below. (The x axis axis in the graph has its tickmarks marked in increments of 2.00 m.) F. (N) 6- B A EL AT Cox (m) -2 Find the work done by the force on the particle as it moves across the following distances. (a) from x = 0 m to x = 8.00 m (b) from x = 8.00 m to x = 12.00 m (c) from x = 0 m to x = 12.00 m Step 1 The work done on the particle by the force F as the particle moves from x = x; to x = x is the area under the curve from x; to x p (a) For x = 0 to x = 8.00 m, WAC = area of triangle ABC SAC x altitude 24 Your response differs from the correct answer by more than 1009%. m )( 8 X Your response differs from the correct answer by more than 10%. Double check your calculations. N) = 6 X Your response differs from the correct answer by more than 10%. Double check your calculations. J. The work done by the force from point A to point C is positive. Submit| |Skip (you cannot come back)4. [0.5/1 Points] DETAILS PREVIOUS ANSWERS SERPSE10 7.4.P.011.MI. When a 4.60-kg object is hung vertically on a certain light spring that obeys Hooke's law, the spring stretches 2.60 cm. (a) If the 4.60-kg object is removed, how far will the spring stretch if a 1.50-kg block is hung on it? 0.00848 When an object is 'hung' from a spring, the spring force is equal in magnitude to the gravitational force. cm (b) How much work must an external agent do to stretch the same spring 4.00 cm from its unstretched position? 1.38 Need Help? Read It Master It Submit Answer 5. [0.5/1 Points] DETAILS PREVIOUS ANSWERS SERPSE10 7.5.P.028. A 7.80 g bullet has a speed of 490 m/s when it hits a target, causing the target to move 4.70 cm in the direction of the bullet's velocity before stopping. (a) Use work and energy considerations to find the average force (in N) that stops the bullet. (Enter the magnitude.) 19923.1 N (b) Assuming the force is constant, determine how much time elapses (in s) between the moment the bullet strikes the target and the moment it stops moving. 0.191 X If the average force is constant, the bullet will have a constant acceleration and its average velocity while stopping is v = (v,+ v)/2, with vy = 0. Use this and the relationship among speed, distance, and time to calculate the elapsed time. s Need Help? Read It