A sphere weighs 200N resting on a wall. It is supported by a rope 20 degrees from the wall. What will be the tension force on the rope?

Resolve T in two components

T(x)= T•sinα,
T(y)= T•cosα.
T(x)/ T(y)= tanα =>
T(x)=T(y) • tanα.
The sphere is at rest:
N =T(x),
mg=T(y)
N/mg= T(x)/T(y) = tanα,
N =mg•tanα =200•0.364=72.8N,
T(x) =72.8.
T=T(x) /sinα =72.8•0.342 = 212.9 N

To find the tension force on the rope, we need to resolve the weight of the sphere into its components.

Step 1: Resolve the weight of the sphere into vertical and horizontal components.
The vertical component of the weight (W_vertical) is given by:
W_vertical = Weight * cos(angle)
W_vertical = 200N * cos(20 degrees)
W_vertical = 200N * 0.9397
W_vertical ≈ 187.94N

The horizontal component of the weight (W_horizontal) is given by:
W_horizontal = Weight * sin(angle)
W_horizontal = 200N * sin(20 degrees)
W_horizontal = 200N * 0.3420
W_horizontal ≈ 68.40N

Step 2: The tension force in the rope (Tension) must exactly balance the horizontal component of the weight.
Therefore, the tension force on the rope will be equal to the horizontal component of the weight.
Tension = W_horizontal ≈ 68.40N

So, the tension force on the rope is approximately 68.40N.

To find the tension force on the rope, we can use the concept of resolved forces. Resolving the weight force of the sphere into two components, one perpendicular to the wall and one parallel to the wall:

1. Perpendicular component (W⊥): This component is equal to the weight of the sphere acting in the downward direction and perpendicular to the wall. It can be calculated using the formula W⊥ = W × cos(θ), where θ is the angle between the weight force and the perpendicular direction (in this case, the angle between the rope and the wall).

W = 200 N (given weight of the sphere)
θ = 20 degrees (given angle)

W⊥ = 200 N × cos(20°) ≈ 188.85 N

2. Parallel component (W‖): This component is equal to the weight of the sphere acting in the downward direction and parallel to the wall. It can be calculated using the formula W‖ = W × sin(θ).

W‖ = 200 N × sin(20°) ≈ 68.56 N

Since the rope is supporting the sphere, the tension force in the rope will be equal and opposite to the parallel component of the weight force.

Therefore, the tension force on the rope is approximately 68.56 N.