A 1kg stone at the end of 1m long string is whirled in a vertical circ...
Answer:
To determine the tension in the string at different points of the vertical circle, we need to analyze the forces acting on the stone.
1. Top of the Circle:
At the top of the circle, the tension in the string will be maximum. This is because the tension needs to provide the centripetal force required to keep the stone in circular motion. In this case, the tension will be equal to the sum of the gravitational force acting on the stone and the centripetal force.
- Gravitational Force: The gravitational force acting on the stone is given by the equation Fg = mg, where m is the mass of the stone and g is the acceleration due to gravity. In this case, Fg = (1 kg) * (9.8 m/s^2) = 9.8 N.
- Centripetal Force: The centripetal force required to keep the stone in circular motion is given by the equation Fc = mv^2/r, where m is the mass of the stone, v is the velocity of the stone, and r is the radius of the circle. In this case, Fc = (1 kg) * (4 m/s)^2 / 1 m = 16 N.
- Tension: The tension in the string at the top of the circle is equal to the sum of the gravitational force and the centripetal force. Tension = Fg + Fc = 9.8 N + 16 N = 25.8 N.
Therefore, the tension in the string at the top of the circle is 25.8 N.
2. Bottom of the Circle:
At the bottom of the circle, the tension in the string will be minimum. This is because the tension only needs to provide the centripetal force required to keep the stone in circular motion. The gravitational force assists in providing this centripetal force. In this case, the tension will be equal to the difference between the gravitational force and the centripetal force.
- Gravitational Force: The gravitational force acting on the stone is still 9.8 N.
- Centripetal Force: The centripetal force required to keep the stone in circular motion is still 16 N.
- Tension: The tension in the string at the bottom of the circle is equal to the difference between the gravitational force and the centripetal force. Tension = Fg - Fc = 9.8 N - 16 N = -6.2 N.
Since tension cannot be negative, we take the magnitude of the tension, which is 6.2 N.
Therefore, the tension in the string at the bottom of the circle is 6.2 N.
3. Halfway Down the Circle:
Halfway down the circle, the tension in the string will be greater than at the bottom but less than at the top. This is because the tension needs to provide the centripetal force required to keep the stone in circular motion, but the gravitational force also assists in providing this force.
- Gravitational Force: The gravitational force acting on the stone is still 9.8 N.
- Centripetal Force: The centripetal force required to keep the stone in circular motion is still 16 N.
- Tension: The tension in the string halfway down the circle is equal to
A 1kg stone at the end of 1m long string is whirled in a vertical circ...