Work done by a variable force Knowledge-Based Practice

Questions

1. 1.

   An object moves along the x-axis under the influence of a variable force given by $F(x) = \frac{10}{(2x + 1)^2}$, where $F$ is in newtons and $x$ is in meters. What is the work done by this force as the object moves from $x = 0\text{ m}$ to $x = 2\text{ m}$?

   • A) 2 J
   • B) 4 J
   • C) 5 J
   • D) 8 J
2. 2.

   A particle moves along the x-axis under the influence of a variable force given by $F(x) = 16 e^{-2x}$, where $F$ is in newtons and $x$ is in meters. What is the total work done by this force as the particle moves from $x = 0\text{ m}$ to $x = \ln(2)\text{ m}$?

   • A) 6 J
   • B) 12 J
   • C) 8 J
   • D) 4 J
3. 3.

   A particle moves along the x-axis under the influence of a variable force given by $F(x) = 8 \cos(2x)$, where $F$ is in newtons and $x$ is in meters. What is the total work done by this force as the particle moves from $x = 0\text{ m}$ to $x = \frac{\pi}{4}\text{ m}$?

   • A) 16 J
   • B) 8 J
   • C) 2 J
   • D) 4 J
4. 4.

   An external force compresses a non-linear spring such that the applied force is given by $F(x) = 80x^3$, where $F$ is in newtons and $x$ is the compression distance in meters. How much work is done by this force to compress the spring from $x = 0\text{ m}$ to $x = 0.50\text{ m}$?

   • A) 10 J
   • B) 5.0 J
   • C) 2.5 J
   • D) 1.25 J
5. 5.

   A particle moves along the x-axis under the influence of a variable force given by $F(x) = 20 - 4x$, where $F$ is in newtons and $x$ is in meters. If the particle starts at $x = 0\text{ m}$, at what position $x > 0$ is the total work done by this force equal to zero?

   • A) 5 m
   • B) 8 m
   • C) 10 m
   • D) 20 m
6. 6.

   An object moves along the x-axis under the influence of a variable force given by $F(x) = 12 - 3x^2$, where $F$ is in newtons and $x$ is in meters. What is the total work done by this force as the object moves from $x = 0\text{ m}$ to $x = 3\text{ m}$?

   • A) 23 J
   • B) 9 J
   • C) -4.5 J
   • D) 22.5 J
7. 7.

   A particle moves along the x-axis under the action of a position-dependent force given by $F(x) = \frac{36}{x^2}$, where $F$ is in newtons and $x$ is in meters. What is the total work done by this force as the particle moves from $x = 2$ m to $x = 6$ m?

   • A) 6 J
   • B) 20 J
   • C) 12 J
   • D) 24 J
8. 8.

   An external force stretches an ideal spring with a force constant of 400 N/m from an initial extension of 0.10 m to a final extension of 0.30 m. What is the total work done by this force during the stretching process?

   • A) 16 J
   • B) 8 J
   • C) 18 J
   • D) 40 J
9. 9.

   A body moves along the x-axis under the influence of a variable force given by $F(x) = 6\sqrt{x}$, where $F$ is in newtons and $x$ is in meters. How much work is done by this force as the body moves from $x = 0$ m to $x = 4$ m?

   • A) 16 J
   • B) 32 J
   • C) 48 J
   • D) 64 J
10. 10.

    A particle moving along the x-axis is acted upon by a force given by $F(x) = 3x^2 + 2x$, where $F$ is in newtons and $x$ is in meters. What is the total work done by this force as the particle moves from $x = 1\text{ m}$ to $x = 3\text{ m}$?

    • A) $34\text{ J}$
    • B) $36\text{ J}$
    • C) $38\text{ J}$
    • D) $26\text{ J}$

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