I have this word problem that I can't figure out. The problem is:
A 15 lb weight is positioned 10 in. form a fulcrum. At what distance from the fulcrum must a 12 lb weigt be positioned to keep the scale balanced?
The substitute that I had today said that the 12 lb. weight would have to be further away from the fulcrum than the 15 lb., but my mom says the opposite.
Sorry, even moms are sometimes wrong
to balance, the (mass x distance) must be equal on each side for a balance
so,
12x = 10x15
x = 12.5 inches
To solve this word problem and determine the distance at which the 12 lb weight should be positioned to balance the scale, we can use the principle of moments or torque.
The principle of moments states that for a balanced scale or lever, the sum of the clockwise moments should be equal to the sum of the counterclockwise moments.
In this case, we have a 15 lb weight positioned 10 inches from the fulcrum. Let's call the distance at which the 12 lb weight is positioned as "x".
To find the distance x, we need to set up an equation using the principle of moments.
The clockwise moment is calculated by multiplying the weight by its distance from the fulcrum. Similarly, the counterclockwise moment is calculated for both weights:
Clockwise moment = 15 lb * 10 in
Counterclockwise moment = 12 lb * x in
Since the scale is balanced, the clockwise moment should be equal to the counterclockwise moment. Therefore, we can set up the equation as follows:
15 lb * 10 in = 12 lb * x in
To solve for x, first divide both sides of the equation by 12 lb:
(15 lb * 10 in) / 12 lb = x in
Now, we can calculate the value of x by evaluating the right side of the equation:
(150 in*lb) / 12 lb = x in
The units of lb cancel out, leaving us with:
(150 in) / 12 = x in
Simplifying the equation further:
12.5 in = x in
Therefore, the 12 lb weight should be positioned 12.5 inches from the fulcrum to balance the scale.
Regarding the disagreement between your substitute teacher and your mom, it seems your mom is correct. The 12 lb weight needs to be further from the fulcrum than the 15 lb weight to maintain the balance.