Question Part
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A 3.25-kg object is attached to a vertical rod by two strings as shown in the figure below. The object rotates in a horizontal circle at constant speed 6.60 m/s.
(a) Find the tension in the upper string.
N
(b) Find the tension in the lower string.
N
To find the tension in the upper and lower strings, we need to analyze the forces acting on the object and use Newton's second law of motion.
(a) To find the tension in the upper string, we need to consider the forces acting on the object in the vertical direction. We can start by analyzing the gravitational force acting on the object:
F_gravity = m * g
where m is the mass of the object and g is the acceleration due to gravity.
Next, we need to consider the net force acting on the object in the vertical direction. Since the object is in circular motion, there is a centripetal force acting towards the center of the circle. This force can be calculated using the equation:
F_centripetal = (m * v^2) / r
where v is the velocity of the object and r is the radius of the circular path.
Since the object is in equilibrium in the vertical direction, the sum of the forces in the vertical direction must be zero:
ΣF_vertical = F_tension_upper + F_tension_lower - F_gravity = 0
From this equation, we can solve for F_tension_upper:
F_tension_upper = F_gravity - F_tension_lower
(b) To find the tension in the lower string, we need to consider the net force acting on the object in the horizontal direction. Again, since the object is in equilibrium, the sum of the forces in the horizontal direction must be zero:
ΣF_horizontal = F_tension_upper - F_tension_lower = 0
From this equation, we can solve for F_tension_lower:
F_tension_lower = F_tension_upper
Therefore, the tension in the lower string is equal to the tension in the upper string.
To find the values for these tensions, we need to know the value of g and the radius of the circular path. These values are not provided in the question, so we cannot calculate the exact tensions. However, the equations provided above can be used once the necessary values are known.