Answer :
Answer:
(B) 143 N
Step-by-step explanation:
Solving the Problem
We must draw a free body diagram (FBD) to find the force tension applied to the mass.
FBD
The mass has a weight force that points directly downward of the mass, and the force applied onto the mass by the two strings points to the top left and top right of the mass, making the same angle (20 degrees) with the horizontal.
Labeling the x and y components of diagonal forces, we see that the x components cancel out by using our knowledge of similar triangles, which leaves us with an FBD of the mass’s weight force pointing downward and the sum of y components pointing up.
Since the mass isn’t moving, the upward force must equal the downward force (this will mean the net force is 0, which is accurate since the mass isn’t accelerating).
So,
2Fy = W. (1)
Solving for F
The force tension in the y direction can be written using trigonometric functions, specifically the sine function.
sin(20) = Fy/F
The diagonal force tension F, can be considered to be the hypotenuse as the picture depicts a right triangle being made with the string, the wall and the horizontal.
We can rearrange this equation to have Fy in terms of F,
Fsin(20) = Fy.
We can substitute this value into the equation (1).
2Fsin(20) = W
Weight force is equal to the product of mass and the gravitational acceleration (9.8m/s²), so
2Fsin(20) = 10(9.8).
Now we solve for F.
2Fsin(20) = 98
Fsin(20) = 49
F = 49 / sin(20) = 143
The force applied to the mass by each of the strings, F is closest to 52 N; option C.
Mass of the object (m) = 10 kg
Angle between each string and the vertical (θ) = 20 degrees
The system is in equilibrium (i.e., the object is not accelerating).
The strings are massless and inextensible.
Gravity (g) is 9.81 m/s².
Step 1: Resolve the forces:
Weight (W): This acts straight downward.
Tension in each string (T): This can be resolved into horizontal and vertical components.
Step 2: Analyze the vertical forces:
The vertical component of each tension (T*cosθ) must balance the weight of the object.
Set up the equation:
2 * T * cosθ = W
Substitute values:
2 * T * cos(20°) = 10 kg * 9.81 m/s²
Solve for T:
T = (10 kg * 9.81 m/s²) / (2 * cos(20°))
T = 52.2 N
