A 45.7-kg boy on a swing moves in a circular arc of radius 3.80 m.At the lowest position, the child's speed reaches 2.78 m/s. Determine the magnitude of the tension in each of the two vertical support chains.
i used mv^2/r, but i keep getting the answer wrong. the answer is suppose to be 270 m/s
please help
A motiom of an objects along the circumference of a circle.
A rock tied to a string is swung around in a circle with a radius of 10 ft. The centripetal acceleration is 16.9 ft/sec2. Calculate the speed of the rock.
To determine the magnitude of the tension in each of the two vertical support chains, you can use the concept of centripetal force.
The centripetal force acting on the boy while he is swinging is provided by the tension in the support chains. At the lowest position of the swing, the centripetal force is equal to the tension force since there is no other force acting in the vertical direction.
The formula to calculate centripetal force is given by:
Fc = (m * v^2) / r
Where:
- Fc is the centripetal force
- m is the mass of the boy (45.7 kg)
- v is the speed of the boy at the lowest position (2.78 m/s)
- r is the radius of the circular arc (3.80 m)
Substituting the given values into the formula:
Fc = (45.7 kg * (2.78 m/s)^2) / 3.80 m
Simplifying the equation:
Fc = (45.7 kg * 7.7284 m^2/s^2) / 3.80 m
Fc = 254.6888 kg·m/s^2 / 3.80 m
Fc = 66.9671 N
Since there are two support chains, the total tension force is twice this value:
Total Tension = 2 * 66.9671 N
Total Tension = 133.9342 N
Therefore, the magnitude of the tension in each of the two vertical support chains is approximately 133.93 N.
Note: The answer you mentioned (270 m/s) seems to be incorrect. The correct value for the tension in each support chain is approximately 133.93 N.