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:

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

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

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

Answer 2

The amount of work that is required to raise one end of the chain is 548.8 Joules.

Given the following data:

• Length of chain = 10 meters.

• Mass of chain = 70 kg.

• Height = 4 meters.

To calculate the amount of work that is required to raise one end of the chain:

How to calculate the work done.

We would solve for the magnitude of the force acting on the chain with respect to the distance and this is given by this expression:

$Force = \frac{mgx}{10} \\\\Force = \frac{70 \times 9.8 \times x}{10}$

Force = 68.6x Newton.

Now, we can calculate the amount of work by using this formula:

$W=\int\limits^{x_2}_{x_1} F({x}) \, dx \\\\W= 68.6 \int\limits^{4}_{0} x \, dx\\\\W= 34.3 x^2 |^4_0\\\\W=34.3 [4^2 -0^]\\\\W=34.3 \times 16$

W = 548.8 Joules.

Read more on work done here: https://brainly.com/question/22599382