Which is the best example of a cycle: a turn of a wheel or a slide down a ski slope?
1 answer:
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The representation of this problem is shown in Figure 1. So our goal is to find the vector 
. From the figure we know that:
From geometry, we know that:
Then using vector decomposition into components:
Therefore:
So if you want to find out <span>how far are you from your starting point you need to know the magnitude of the vector, that is:
</span>
Finally, let's find the <span>compass direction of a line connecting your starting point to your final position. What we are looking for here is an angle that is shown in Figure 2 which is an angle defined with respect to the positive x-axis. Therefore:
</span>
From geometry, we know that:
Then using vector decomposition into components:
Therefore:
So if you want to find out <span>how far are you from your starting point you need to know the magnitude of the vector
</span>
Finally, let's find the <span>compass direction of a line connecting your starting point to your final position. What we are looking for here is an angle that is shown in Figure 2 which is an angle defined with respect to the positive x-axis. Therefore:
</span>
Answer: Work Done would remain same.
Let us assume that the velocity is constant while taking the load up the inclined plane. Then, the kinetic energy would remain the same. This is because kinetic energy is dependent on velocity . If that is constant, the kinetic energy would remain same. The potential energy is dependent on the height
. If the height is changed, then potential energy varies. In the question, it is mentioned that without changing the height, the length of the inclined plane is changed. Therefore, the potential energy would be same as before.
We know, work done is equal to potential energy plus kinetic energy. Since there is no change in any of these, the required work done would not change.