doing webwork when i came across this question. sure i had it right but apparently im not.
The weightless horizontal bar in the figure below is in equilibrium. Scale B reads 4.20 kg (N.B. as you know, the scale should read N, but no one told the manufacturer). The distances in the figure (which is not to scale) are: D1 = 8.5 cm, D2 = 9.0 cm, and D3 = 5.0 cm. The mass of block X is 0.91 kg and the mass of block Y is 1.97 kg. Determine the reading on scale A. and mass of block Z.
(look up "massless beam torque and 2 scale" and itll be the fourth pic on google)
I made the spot where z and scale b is, the center of rotation therefore.
Net torque= -Ta + Tx + Ty = 0
-(0.09+0.085+0.05)Ta = -(0.05+0.09)(0.91*9.8)+(0.05)(1.97*9.8)
(excluded sin(angle) because all angles are 90 degrees)
-0.14Ta =_ (1.24852+0.9653)
Ta = 9.8392 N or in this case; 9.8392 kg.
I cant solve for the second question until i get the first answer.
nevermind. figured out that the "mass" of the blocks are actually the weight so i unnecessarily multiplied them by 9.8
To solve for the reading on scale A and the mass of block Z in the given problem, you correctly set up the equation for the net torque:
Net torque = -Ta + Tx + Ty = 0
You identified the center of rotation correctly as the point where block Z and scale B are located. Great job!
Now, let's proceed to solve for the reading on scale A (Ta). Your equation for net torque is as follows:
-0.14Ta = (1.24852 + 0.9653)
To solve for Ta, we can start by isolating the variable:
Ta = -((1.24852 + 0.9653) / 0.14)
Simplifying the right side of the equation:
Ta ≈ -16.693
The negative sign indicates that the reading on scale A (Ta) is directed in the opposite direction compared to the other forces. However, since scale readings cannot be negative, we take the absolute value of Ta:
Ta ≈ 16.693 N
So the reading on scale A is approximately 16.693 N.
Now, let's solve for the mass of block Z. We know that weight is equal to mass multiplied by the acceleration due to gravity, which is approximately 9.8 m/s^2. The equation for the weight of an object is given by:
Weight = mass × acceleration due to gravity
Considering block Z, we have:
Weight of block Z = Reading on scale B = 4.20 kg
So, the weight of block Z is 4.20 kg.
Since weight equals mass multiplied by the acceleration due to gravity, we can write the equation as:
mass of block Z × 9.8 = 4.20
Solving for the mass of block Z:
mass of block Z = 4.20 / 9.8
mass of block Z ≈ 0.429 kg
Therefore, the mass of block Z is approximately 0.429 kg.
In conclusion, the reading on scale A is approximately 16.693 N, and the mass of block Z is approximately 0.429 kg.