Problem 2- A 4 kg object is attached to a vertical rod by two strings, as in the Figure. The object rotates in a horizontal circle at constant speed 6 m/s. Find the tension in (a) the upper string and (b) the horizontal string.
without the figure...
http://people.physics.tamu.edu/kattawar/solutions%20218h%20exam2%20f11.PDF
http://www.csupomona.edu/~skboddeker/131/131hw/ch6h.htm
Thank you very much Elena
To find the tension in the upper string, we need to consider the forces acting on the object in the vertical direction.
Let's denote the tension in the upper string as T1 and the tension in the horizontal string as T2.
(a) To find T1, we need to consider the vertical forces acting on the object. There are two forces acting vertically: the weight (mg) and the tension in the upper string (T1).
The object is moving in a horizontal circle at a constant speed, which means it is experiencing centripetal acceleration towards the center of the circle. This centripetal acceleration is provided by the tension in the horizontal string (T2).
Since the object is not accelerating vertically, the sum of the vertical forces must be zero:
T1 - mg = 0
Therefore, T1 = mg.
(b) To find T2, we need to consider the horizontal forces acting on the object. The only horizontal force is the tension in the horizontal string (T2), which is responsible for providing the centripetal acceleration towards the center of the circle.
The centripetal force (Fc) can be calculated using the formula:
Fc = (mass * velocity^2) / radius
In this case, the mass of the object is 4 kg, the velocity is 6 m/s, and the radius is not given. We need to find the radius of the circular motion.
To find the radius, we can use the formula for centripetal acceleration (ac):
ac = velocity^2 / radius
Since the object is moving in a horizontal circle at a constant speed, the centripetal acceleration is given by:
ac = velocity^2 / radius
6^2 = (6^2) / radius
36 = 36 / radius
Multiplying both sides by radius:
36 * radius = 36
Dividing both sides by 36:
radius = 1 meter
Now that we have the radius, we can calculate the centripetal force (Fc):
Fc = (mass * velocity^2) / radius
Fc = (4 * 6^2) / 1
Fc = 144 N
Since T2 provides the centripetal force, T2 = Fc:
T2 = 144 N.
Therefore, the tension in (a) the upper string is 4 kg * 9.8 m/s^2 = 39.2 N, and the tension in (b) the horizontal string is 144 N.