<p>A worker can lift a box a vertical distance of 1m or roll it up a two meter-long ramp to the same elevation. Either way he does the same amount of work. If he uses the ramp, the applied force required is how much of the force that if he doesn't use the ramp?</p>
<p>I think you have the wrong forum…</p>
<p>I’m pretty sure it’s one half, someone wanna confirm?</p>
<p>Work is force times distance. So if the amount of work is the same for both, the force times the distance must be the same for both.</p>
<p>F1 x 1m = F2 x 2m</p>
<p>So the force with the ramp is one half the force without the ramp.</p>
<p>But doesn’t the angle from the vertical axis need to be taken into account?</p>
<p>The work of the ramp situation must be F1<em>1. But the applied force can change because work equals F dot d or F</em>d*cos(angle from axis). We can’t answer this question unless the angle is provided.</p>
<p>you got it right.
assuming it is frictionless, whatever amount of work you do will be translated into the potential energy. Since the elevation is the same, both have the same potential energy.
and with pythagorean theorem, you can confirm that on the ramp, your pushing force is gonna be 5 n and the distance is 2m
so 10 x 1m = 5N x 2m
Either way, its the same</p>
<p>we also know the measurements of triangle since we know the hypotenuse and height, we can get the angle as well its 30 60 90 triangle</p>
<p>Ya. 1/2 obviously.
In other words:</p>
<p>mgsin0 x 2 = mg x 1
2mgsin0=mg
2sin0=1
sin0=0.5
0=30</p>
<p>the angle is 30 degrees LOL or you can always just draw a 30/60/90 triangle.</p>
<p>OR you can not be a noob and skip the ***<em>ing trigonometry and just remember work=force</em>distance.</p>
<p>Buddy the guy was talking about the angle so ya…
I think it’s pretty obvious it’s 1/2. Everyone knows that by now.</p>
<p>Why does the angle matter?</p>
<p>Obviously we know the answer, but you guys over-complicate the problem ridiculously.</p>
<p>Since the box is at the same final height in both cases the gravitational potential energy is the same in both cases, thus the change in potential energy is the same, thus the work is the same. In the first case the distance is equal to the elevation (1 m) because the box was lifted straight up. In the second case the distance is equal to 2 m because that is the length of the ramp. Since Work = Force * Distance, and the work is the same, while the distance is doubled in the second case it means that the average force in the second case must be equal to 1/2 the distance in the first case.</p>