A 1.7 -kg object attached to the end of a string swings in a vertical circle (radius = 80 cm). At the top of the circle the speed of the object is 26.0 m/s. What is the magnitude of the
tension in the string at this position?
m (v^2/r - 9.81)
To find the magnitude of the tension in the string at the top position of the circle, we need to consider the forces acting on the object.
1. Start by calculating the gravitational force acting on the object at the top of the circle using the formula:
F_gravity = m * g
Where:
m = mass of the object = 1.7 kg
g = acceleration due to gravity ≈ 9.8 m/s^2
Substituting the values, we get:
F_gravity = 1.7 kg * 9.8 m/s^2
2. The tension in the string provides the centripetal force required to keep the object moving in a circle. At the top of the circle, the net force is the sum of the tension and the gravitational force. Hence,
F_net = F_tension + F_gravity = m * v^2 / r
Where:
F_tension = tension in the string (the value we need to find)
m = mass of the object = 1.7 kg
v = velocity of the object = 26.0 m/s
r = radius of the circle = 80 cm = 0.8 m (converted to meters)
Rearranging the equation, we have:
F_tension = m * v^2 / r - F_gravity
3. Now, substitute the given values into the equation and calculate:
F_tension = (1.7 kg * (26.0 m/s)^2) / 0.8 m - (1.7 kg * 9.8 m/s^2)
Solving the equation, we get:
F_tension ≈ 116.15 N
Therefore, the magnitude of the tension in the string at the top of the circle is approximately 116.15 N.
To find the magnitude of the tension in the string at the top of the swing, we can use the principles of centripetal force and gravitational force.
1. Start by determining the net force acting on the object at the top of the swing. At this position, the only two forces acting on the object are tension (T) and weight (mg).
2. The net force acting on the object is the centripetal force required to keep the object in circular motion. It can be calculated using the equation:
Net force = T - mg
3. The centripetal force can be calculated using the equation:
Centripetal force = (mass × velocity^2) / radius
4. Now, substitute the given values into the equations:
Centripetal force = (1.7 kg × 26.0 m/s^2) / 0.8 m
Net force = T - (1.7 kg × 9.8 m/s^2)
5. Equate the centripetal force to the net force, and solve for T:
(1.7 kg × 26.0 m/s^2) / 0.8 m = T - (1.7 kg × 9.8 m/s^2)
6. Simplify and solve the equation for the tension (T).