Work done by a variable force Transitional Reasoning Practice

Questions

1. 1.

   An experimental launch carriage accelerates a payload along a straight horizontal track from x = 0 m to x = 16 m. The forward drive force increases linearly from 0 N at x = 0 m to 800 N at x = 10 m, and then decreases linearly from 800 N to 200 N between x = 10 m and x = 16 m. What is the total work done by the drive force on the payload over this displacement?

   • A) 7000 J
   • B) 6400 J
   • C) 5800 J
   • D) 11 000 J
2. 2.

   During a performance test of an automated transport cart on a straight rail, a mechanical actuator applies a position-dependent net force given by $F(x) = 3x^2 - 2x$, where $F$ is in newtons and $x$ is in meters. The cart moves along the positive x-axis from an initial position of $x = 1\text{ m}$ to a final position of $x = 3\text{ m}$. What is the total work done by this variable force on the cart over this interval?

   • A) 42 J
   • B) 20 J
   • C) 18 J
   • D) 12 J

Answers and step-by-step solutions appear after you finish the test.