Question

A chain lying on the ground is 10 m long and its mass is 70 kg. How much work (in J) is required to raise one end of the chain to a height of 4 m?

Answer 1

Answer:

$W= 34.3 \frac{kg}{s^2} (4^2-0^2)m^2 =548.8 \frac{kg m^2}{s^2} =548.8 J$

Step-by-step explanation:

Data Given: m = 70 kg , g = 9.8 ms^-2, h =10m.

For this case we can use the following formula:

$W = \int_{x_i}^{x_f} F(x) dx$

For this case we need to find an expression for the force in terms of the distance. And since on this case the total distance is 10 m long we can write the expression like this:

$F(x) = \frac{ma}{10m}= \frac{mg}{10m} x$

The only acceleration on this case is the gravity and if we replace the values given we got:

$\frac{70 kg *9.8 m/s^2}{10m} x=68.6 x\frac{kg}{s^2}$

Now we can find the required work with the following integral:

$W= 68.6 \frac{kg}{s^2} \int_{0}^4 x dx$

$W= 34.3 \frac{kg}{s^2} x^2 \Big|_0^4$

$W= 34.3 \frac{kg}{s^2} (4^2-0^2)m^2 =548.8 \frac{kg m^2}{s^2} =548.8 J$