Question

The table shows the dimensions of four wedges.

A 3-column table with 4 rows. The first column has entries W, X, Y, Z. The second column labeled thickness at widest part (inches) has entries 2, 4, 3, 5. The third column labeled slope (inches) has entries 5, 8, 9, 10.

Which wedge requires the least amount of force to do a job?

W
X
Y
Z

Answer 1

The correct answer is Y not Z.

Explanation:

Answer 2

Wedge Z requires the least amount of force to do a job.

Explanation:

In physics, Work is defined as the energy needed to move certaing object through a certain distance. Specifically, the work done is directly proportional to the force exerted and the distance.

It's important to know that a change of point is needed to have actually work done, physically speaking. This means if the object doesn't move, then there's no work done.

Mathematically, the work is defined

`W= F * d`

Isolating the force

`F=(W)/(d)`

So, notice that the distance is inversely proportional to the force needed, which means the less distance, more force we need.

Now, the problem is giving wides and slopes, which we can use to find heights. And we know already that the less distance we have, the greater force we need, or the most distance, the least force.

Let's find which wedge has the greatest vertical distance.

`m=(y)/(x)`

Wedge 1.

`5=(y)/(2) \implies y=10`

Wedge 2.

`8=(y)/(4) \implies y=32`

Wedge 3.

`9=(y)/(3) \implies y=27`

Wedge 4.

`10=(y)/(5)\\ y=50`

Notice that the last wedge has greater vertical distance, that means Wedge Z requires least amount of force to do a job.