Answer:
Explanation:
ball's weight = mg = .5 x 9.8 = 4.9 N.
If T₁ be tension at the top , centripetal force provided at the top
= mg + T₁ = 4.9 + T₁
4.9 + T₁ = m v² / r , v = velocity at the top , r = radius of circular path = 1.02 m
4.9 + T₁ = .5 x 4² / 1.02
4.9 + T₁ = .5 x 4² / 1.02
= T₁ = 7.843 - 4.9 = 2.943 N
If T₂ be tension at the bottom , centripetal force provided at the bottom
= T₂ - mg = T₂ - 4.9
T₂ - 4.9 = m v² / r , v = velocity at the bottom , r = radius of circular path = 1.02 m
T₂ - 4.9= .5 x 7.5² / 1.02
T₂ - 4.9 = .5 x 7.5² / 1.02
T₂ = 32.47 N
This question involves the concepts of tension, centripetal force and the weight force of the ball.
A) The weight of the ball is "4.91 kg".
B) The tension in the string when the ball is at the top is "2.93 N".
C) The tension in the string when the ball is at the bottom is "32.48 N".
A)
The weight of the ball can be found using the following formula:
W = mg
where,
W = weight = ?
m = mass = 500 g = 0.5 kg
g = acceleration due to gravity = 9.81 m/s²
Therefore,
W = (0.5 kg)(9.81 m/s²)
W = 4.91 N
B)
At the top of the circle, the weight and the tension force shall be acting downwards on the ball while the centripetal force shall be balancing them in the upward direction. Therefore,
[tex]W+T =F_c\\\\W+T =\frac{mv^2}{r}[/tex]
where,
T = tension at top = ?
v = veloity at top = 4 m/s
r = radius of circle = 102 cm = 1.02 m
Therefore,
[tex]4.91\ N +T=\frac{(0.5\ kg)(4\ m/s)^2}{1.02\ m}\\\\T = 7.84\ N - 4.91\ N\\[/tex]
T = 2.93 N
C)
At the bottom of the circle, the weight and the centripetal force shall be acting downwards on the ball while the tension force shall be balancing them in the upward direction. Therefore,
[tex]W+F_c =T\\\\T =\frac{mv^2}{r}+W\\\\[/tex]
where,
T = tension at bottom = ?
v = veloity at bottom = 7.5 m/s
r = radius of circle = 102 cm = 1.02 m
Therefore,
[tex]T=\frac{(0.5\ kg)(7.5\ m/s)^2}{1.02\ m}+4.91\ N\\[/tex]
T = 32.48 N
Learn more about centripetal force here:
brainly.com/question/11324711?referrer=searchResults
The attached picture shows the free-body diagram of the situation.
