Work done by a variable force Knowledge-Based Download PDF

Questions

1. 1.

   A 2.0 kg particle moves along the x-axis with a position-dependent speed given by $v(x) = 3x$, where x is in meters and v is in meters per second. What is the net work done by the variable force acting on the particle as it moves from x = 1.0 m to x = 3.0 m?

   • A) 72 J
   • B) 36 J
   • C) 24 J
   • D) 81 J
2. 2.

   A particle moves in the $xy$-plane from the origin $(0, 0)$ to the position $(3\text{ m}, 2\text{ m})$ under the action of a force $\vec{F} = (4x)\hat{i} + (6y^2)\hat{j}$, where $x$ and $y$ are in meters and $\vec{F}$ is in newtons. What is the total work done by this force on the particle?

   • A) 24 J
   • B) 28 J
   • C) 30 J
   • D) 34 J
3. 3.

   A non-linear spring requires an applied force of $F(x) = 80x^3$ to maintain an extension $x$, where $F$ is in newtons and $x$ is in meters. What is the total work done by this force to stretch the spring from x = 1 m to x = 2 m?

   • A) 120 J
   • B) 240 J
   • C) 560 J
   • D) 300 J
4. 4.

   A particle moving along the x-axis is acted upon by a variable force $F(x) = 30 - 5x$, where $F$ is in newtons and $x$ is in meters. What is the total work done by this force as the particle moves from $x = 0$ m to the position where the force first becomes zero?

   • A) 45 J
   • B) 60 J
   • C) 90 J
   • D) 180 J
5. 5.

   A uniform cable of mass 8.0 kg and length 5.0 m hangs vertically from the edge of a platform. How much work is done against gravity by an external lifting force to pull the entire cable onto the platform at a constant speed? (Take g = 9.8 m/s2.)

   • A) 392 J
   • B) 294 J
   • C) 98 J
   • D) 196 J
6. 6.

   A particle moves along the x-axis from $x = 0$ m to $x = \pi$ m under the action of a force given by $F(x) = 8\sin(x)$, where $F$ is in newtons and $x$ is in meters. What is the total work done by this force on the particle?

   • A) 0 J
   • B) 16 J
   • C) 8 J
   • D) -16 J
7. 7.

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

   • A) 16 J
   • B) 24 J
   • C) 48 J
   • D) 32 J
8. 8.

   An ideal spring has a spring constant of 250 N/m. How much work must be done by an external force to stretch the spring from an extension of 0.20 m to 0.40 m?

   • A) 5.0 J
   • B) 10 J
   • C) 15 J
   • D) 20 J
9. 9.

   An object moves along the x-axis from $x = 1$ m to $x = 5$ m under the action of a force directed along the displacement given by $F(x) = \frac{10}{x^2}$, where $F$ is in newtons and $x$ is in meters. What is the work done by this force on the object?

   • A) 8 J
   • B) 12 J
   • C) 2 J
   • D) 40 J
10. 10.

    A particle moves along the x-axis from x = 1 m to x = 2 m under the action of a force given by $F(x) = 3x^2 + 4x$, where F is in newtons and x is in meters. What is the total work done by this force on the particle?

    • A) 13 J
    • B) 16 J
    • C) 19 J
    • D) 20 J