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The mass of the object will be 20 kg
What would be the mass of object shown?
First, create a free-body diagram for the item and label it. I've included a drawing I made that depicts all the relevant forces at work on the object.
The tension forces (T1 and T2), their x and y components, and the weight force are shown on the free-body diagram (w).
In order to apply this angle later in the issue to determine the object's mass using Newton's Second Law, we want to start by determining the angle theta ().
By utilizing the knowledge that there are no imbalanced horizontal forces acting on the item and that the net force is zero, we can determine the angle.
This implies that T1 sin(40) = T2 sin(). Create an equation with them equal to one another and find the angle. The tension forces are provided as T1 = 34 N and T2 = 24 N.
T1 sin(40) equals T2 sin().
220 * sin() = 135 * sin(40).
To determine sin(), multiply 135 by sin(40) and divide the result by 220.
0.3944378513 = sin(Θ)
Consider both sides of the equation's inverse sine.
Θ = sin⁻¹(0.3944378513) (0.3944378513)
Θ = 23.2309189°
Now that we have the angle, we can utilize it to construct a mass-related equation according to Newton's Second Law.
We are aware that the object is subject to a weight force that is applied downward and is equal to mg (mass divided by the gravitational acceleration).
The two tension forces' x-components are the two forces pushing upward on the item.
Since the item is not moving vertically, we may infer that the net force must be zero (F = ma, and since there is no acceleration, F = 0 N).
The forces acting in the y-direction added together will equal zero. We can construct the following equation by making the upward direction positive and the descending way negative:
F is equal to T1 cos(40) plus T2 cos(23.2309189) - mg = 0.
Weight force (mg) should be added to both sides of the equation.
T2 cos(23.2309189) + T1 cos(40) = mg
Change T1 to 135 and T2 to 220.
220 * cos(23.2309189) + 135 * cos(40) = mg
On Earth, the gravitational acceleration is 9.8 m/s2. To find the object's mass, m, solve the problem using this number as a substitute.
220 * cos(65.59058699) + 135 * cos(40) = m (9.8)
Analyze the equation's left side.
194.30766 = 9.8m
M = 19.829, multiply both sides of the equation by 9.8.
Since the problem provides us with the tension forces as two significant values, round this to two.
m ≈ 20 kg
The object in the image weighs about 20 kg.
Know more about tension:
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