(D) The work done $W$ by a variable force $F$ is given by the integral of the force with respect to displacement: $W = \int_{x_1}^{x_2} F \cdot dx$ Gi

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(D) The work done $W$ by a variable force $F$ is given by the integral of the force with respect to displacement: $W = \int_{x_1}^{x_2} F \cdot dx$ Given $F = (g - x^2) \text{ N}$ and $g = 10 \text{ m/s}^2$, the force becomes $F = (10 - x^2) \text{ N}$. Integrating from $x = 0$ to $x = 3$: $W = \int_{0}^{3} (10 - x^2) dx$ $W = [10x - \frac{x^3}{3}]_{0}^{3}$ $W = (10(3) - \frac{3^3}{3}) - (10(0) - \frac{0^3}{3})$ $W = (30 - \frac{27}{3}) - 0$ $W = 30 - 9 = 21 \text{ J}$

Class 11 Physics Work, Energy, Power and Collision Work Done by Variable Force and Force-Displacement Graph

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$A$ horizontal force $F = (g - x^2) \hat{i} \text{ N}$ acts on a wooden block resting on a horizontal smooth surface. The work done to move the block from $x = 0$ to $x = 3 \text{ m}$ (in $\text{J}$) is (Use $g = 10 \text{ m/s}^2$)

TS EAMCET 2021 All TS EAMCET

A
$24$
B
$35$
C
$30$
D
$21$

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Work, Energy, Power and Collision

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Work Done by Variable Force and Force-Displacement Graph

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$A$ horizontal force $F = (g - x^2) \hat{i} \text{ N}$ acts on a wooden block resting on a horizontal smooth surface. The work done to move the block from $x = 0$ to $x = 3 \text{ m}$ (in $\text{J}$) is (Use $g = 10 \text{ m/s}^2$)

Similar Questions

Power delivered to a mass is $P = (3t^2 - 2t + 1) \text{ W}$. The change in kinetic energy from $t = 2 \text{ s}$ to $t = 4 \text{ s}$ is: .................... $J$

$A$ force $\vec F = k(y\hat i + x\hat j)$ where $k$ is a positive constant acts on a particle moving in the $x-y$ plane. The particle moves along a straight line from the point $(3, 5)$ to $(5, 7)$. The work done by the force is: ............... $k$

$A$ force is applied to a particle of mass $0.1 \ kg$ as a function of distance as shown in the figure. If it starts from rest at $x = 0$,its velocity at $x = 12 \ m$ is ....... $m/s$.

The potential energy $U(x)$ of a system is represented in the figure. The force $F(x)$ acting on the system will be represented by:

The graph of resistive force versus displacement for an object of mass $25 \ kg$ is given. If its velocity at $x = 0$ is $2 \ m/s$,then its kinetic energy at $x = 4 \ m$ is ..... $J$.

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