Answer:
a. 14.6 N
b. 0.688 m/s
Step-by-step explanation:
Draw a free body diagram. There are two forces acting on the ball: tension force along the string, and weight force downward.
a. Sum of the forces in the y-direction:
∑F = ma
T cos θ − mg = 0
T = mg / cos θ
T = (1.45 kg) (9.8 m/s²) / cos 14°
T = 14.6 N
b. Sum of the forces in the x-direction (towards the center):
∑F = ma
T sin θ = m v² / r
(mg / cos θ) sin θ = m v² / r
mg tan θ = m v² / r
g tan θ = v² / r
v = √(gr tan θ)
v = √(9.8 m/s² (0.80 m sin 14°) tan 14°)
v = 0.688 m/s