Respect Responsibility Readiness
1.
Mae Dupp weighted 120
pounds and sat on one end of a teeter-totter 8 feet from the center. Fess Dupp
weighted 160 pounds and sat on the other side. How far (in feet) from the
fulcrum (balance point) must Fess sit to balance point is at the center of the
board?
Solution
Read the problem and determine the unknown. The question asks how far from the fulcrum Fess sits, so
Let x = Fess's distance from fulcrum in feet.
Mae weighs 120 pounds and sits on one end of the teeter-totter.
Mae sits 8 feet from the center.
Fess weighed 160 pounds and sat on the other side. We have already found that we would let x equal Fess's distance.
w1d1 = w2d2 where w is weight and d is distance.
w1 = 120 d1 = 8 w2 = 160 d2 = x
120(8) = 160x
960 = 160x
x = 6
So Fess must sit 6 feet from the fulcrum.
2.
Bill Ding was digging up
his yard to plant a garden. He hit a large rock and got a crowbar to raise the
rock to the surface. The crowbar was 6 feet long and the rock was later found to
weigh 80 pounds Bill used another rock as the fulcrum and exerted a force equal
to 16 pounds on th
Solution
Read the problem and determine the unknown. The question asks how far from the fulcrum Fess sits, so
Let x = distance in feet of 80-pound rock from fulcrum.
Equation
w1d1 = w2d2 where w is weight and d is distance.
w1 = 16 d1 = 6 - x w2 = 80 d2 = x
16(6 - x) = 80x
96 - 16x = 80x
-96x = -96
x = 1
So the fulcrum was 1 foot from the rock.
3. A weight of 60 pounds rests
on the end of an 8-foot lever and is 3 feet from the fulcrum. What weight must
be placed on the other end of the lever to balance the 60-pound weight?
Let x = unknown weight in pounds
Diagram
5x = 60(3) = 180
x = 36
Answer
A 36 pound weight will balance the 60 pound weight
4. Four girls decided to use
the same teeter-totter. Two of them weighing 75 pounds and 50 pounds,
respectively, sat on opposite ends of the 12-foot board which had the balance
point at the center. The third girl weighting 60 pounds got on the same side as
the one weighing 50 pounds and sat 5 feet from the fulcrum. Where must the
fourth girl sit so the teeter-totter is balanced if she weighs 40 pounds?
Let x = unknown weight in pounds
Diagram
5x = 60(3) = 180
x = 36
Answer
A 36 pound weight will balance the 60 pound weight
5. A 200-pound weight rests on
one end of a lever, 12 feet from the fulcrum. What weight, resting on the
opposite end and 3 feet from the fulcrum, would make a balance?
6.
The
boys take a 12-foot-long board and rest it on a large rock to make a
teeter-totter. If the boys sit on opposite ends of the board and weigh 50 pounds
and 70 pounds, respectively, how far from the fulcrum will the 70-pound boy be
if they balance?
7.
A
window in Patty O’ Cover house is stuck. She takes an 8-inch screwdriver to
pry open the window. If the screwdriver rests on the sill (fulcrum) 3 inches
from the window and Patty O’ Cover has to exert a force of 10 pounds on the
other end to pry open the window, how much force was the window exerting?
8.
A
35-pound weight is 2 feet from the fulcrum, and a 75-pound weight on the same
side is 10 feet from the fulcrum. If a weight on the other end 6 feet from the
fulcrum balances the first two, how much does it weigh?
9.
A
lever 10 feet long has a 100-pound weight on one end and a 150-pound weight on
the other. If the fulcrum is in the center, in what location must an 80-pound
weight be placed so that the lever will balance?
10. Batman and Robin go out to play. Batman, who weighs 90 pounds, sits on one end of a 14-foot teeter-totter. Its balance point is at the center of the board. Robin, who weighs 120 pounds, climbs on the other end and slides toward the center until they balance. What is Robin’s distance from her end of the teeter-totter when they balance?