How to you set up the equation for this problem and how to solve it?
Topic: How to you set up the equation for this problem and how to solve it?
July 19, 2019 / By Zachery Question:
Physics help please: A uniform meterstick pivoted at its center, has a 100 g mass suspended at 25 cm position,
at what position should a 75 g mass be suspended to put the system in equilibrium?
what mass will have to be suspended at the 90 cm position for the system to be in equilibrium?
Best Answers: How to you set up the equation for this problem and how to solve it?
Shimea | 9 days ago
The sum of the torques = 0
Torque = Force * lever arm
We first must convert 100g mass under gravity to a force
F = MA where A = 9.8 m/s^2 and M is in kilograms
F = 0.1kg * 9.8 m/s^2 = 0.98 Newton
Torque = 0.98 N * (50 - 25) cm = 24.5 N - cm (a weird unit but we will keep it. You teacher might have wanted you to convert the 25 cm to 0.25 meters but that is not necessary if we keep our units straight)
That torque is counter-clockwise 24.5 N -cm
We need to balance that with 75 grams placed on the other side of the pivot to give us a clockwise torque to balance our CCW torque
Again convert grams mass to force
F = 0.075 * 9.8 = 0.735 N
We need a torque of 24.5
24.5 = 0.735 * lever arm
Lever arm = 24.5/0.735 = 33.333 cm
Location: 50 + 33. 33 = 83.33 cm mark (33.33 cm from the center)
Again we need to generate the same torque with a lever arm of (90 - 50) = 40 cm
24.5 = Force * 40
Force = 0.6125 N
F = Mass * Gravvity
0.6125 = Mass * 9.8
Mass = 0.0625 Kg = 62.5 grams
👍 246 | 👎 9
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we use the idea that clockwise moments = anticlockwise moments for a system in equilibrium.
also we have to use distances from the pivot. the pivot being at the 50 cm mark as it is a meter rule
for the first problem:
100 * 25 = 75 * X
X = (100*25) / 75
= 33.3cm (distance from pivot)
so it needs to be placed at the point 88.3 cm on the rule (which is 33.3 cm from the pivot at 50 cm)
for the second problem:
100*25 = (90 - 50) * X
X = (100*25) / 40
X = 62.5g
👍 100 | 👎 7
ΣM = 0 is the eq to use.
To simplify the problem, choose the center of the stick as the zero point.
a) 100*(50-25) = 75*(X-50) where X is in cm
b) 100*(50-25) = X*(90-50) where X is in grams
👍 92 | 👎 5
exceedingly lots each and every thing could be became right into a mathematical equation, yet some equations could be so complicated, that your techniques might turn to mush only thinking approximately it (there is an equation to describe that, too). So exceedingly lots each and every physique of life's problems could be defined by way of math, this is genuine.
👍 84 | 👎 3
Originally Answered: Set up an equation and solve the following problem.?
x^2 + x^2 + 2x + 1 = 13
2x^2 + 2x - 12 = 0
x^2 + x - 6 = 0
(x + 3)(x - 2) = 0
x = -3 , 2
Edit: I deleted "none of the above", here is the explanation:
-3 + 1 = -2
-3 and -2 are the first two consecutive whole numbers that satisfy the condition, but since they are not listed as an option, then a) 2 , 3 is an acceptable answer.
Note: If you know and/or consider the fact that negative integers are also whole numbers, please accept my sincere apologies since I wrongfully thumb downed all the answers based on the assumption that they believe otherwise.