Respuesta :
Answer:
f = 63.8 N
Explanation:
initial angle to the vertical = 5 degrees
initial holding force = 40 N
final angle to the vertical = 8 degrees
final holding force = ?
find the final holding force
- force = mgSinθ
m = mass and g = acceleration due to gravity
- for the initial holding force:
40 = mgSin5
mg = [tex]\frac{40}{sin5}[/tex] ....equation 1
- for the final holding force:
f = mgSin8 ......equation 2
substituting the value of mg from equation 1 (where mg = [tex]\frac{40}{sin5}[/tex] ) into equation 2
f = mgSin8 = [tex]\frac{40}{sin5}[/tex] x Sin8
f = 63.8 N
Answer:
64 N
Explanation:
Given that the angles are very small, the following approximation can be made:
F ≈ m*g*α
where F is the force needed to hold the ball, m is the ball mass, g is the acceleration of gravity and α is the angle between the cord and the vertical.
Let's call F1 the force needed to hold the ball at 5° (α1) and F2 the force needed to hold the ball at 8° (α2).
F1 ≈ m*g*α1
F2 ≈ m*g*α2
Dividing the equations:
F1/F2 = α1/α2
F2 = (α2/α1)*F1
F2 = (8/5)*40
F2 = 64 N