A block of mass $10 \mathrm{~kg}$ is moving along $\mathrm{x}$-axis under the action of force $F=5 x~ N$. The work done by the force in moving the block from $x=2 m$ to $4 m$ will be __________ J.
Answer (integer)
30
Solution
To calculate the work done by the force $F = 5x$ in moving the block from $x = 2m$ to $x = 4m$, we can use the formula for work done by a variable force:
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$W = \int_{x_1}^{x_2} F(x) dx$
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In this case, $F(x) = 5x$, $x_1 = 2m$, and $x_2 = 4m$. Now, we can substitute these values into the formula and evaluate the integral:
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$W = \int_{2}^{4} 5x dx$
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To evaluate the integral, we find the antiderivative of $5x$:
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$\int 5x dx = \frac{5}{2}x^2 + C$
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Now, we can find the work done by evaluating the antiderivative at the limits of integration:
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$W = \left[\frac{5}{2}x^2\right]_{2}^{4} = \frac{5}{2}(4^2) - \frac{5}{2}(2^2)$
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$W = \frac{5}{2}(16) - \frac{5}{2}(4) = 40 - 10 = 30 \mathrm{J}$
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The work done by the force in moving the block from $x = 2m$ to $x = 4m$ is 30 J.
About this question
Subject: Physics · Chapter: Work, Energy and Power · Topic: Work Done by a Force
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