Final answer:
To make a full circle on a swing, the child needs to have a minimum speed at the top of the swing. The minimum speed can be calculated using the concept of centripetal acceleration. At the top of the swing, the child's apparent weight can be found by considering the centripetal force. The apparent weight at the bottom of the swing can also be calculated using the same approach.
Step-by-step explanation:
To make a full circle on the swing, the child must have a minimum speed at the top of their path. This can be calculated using the concept of centripetal acceleration. The formula is a = v^2 / r, where a is the centripetal acceleration, v is the velocity, and r is the radius of the circular path. In this case, the radius is equal to the length of the swing, L. So, the centripetal acceleration would be a = v^2 / L. To calculate the minimum speed, we need to find the maximum acceleration. The maximum acceleration that a child can withstand without falling off is about 4 times the acceleration due to gravity, or 4g. Therefore, the minimum speed would be the square root of 4g * L.
To find the apparent weight of the child at the top of the swing, we need to consider the centripetal force. The centripetal force is given by the formula F = m * a, where F is the force, m is the mass, and a is the centripetal acceleration. At the top of the swing, the force will be the sum of the gravitational force and the centripetal force. So, we have F = mg + m * a. To find the apparent weight, we subtract the actual weight, mg, from the total force, mg + ma.
At the bottom of the swing, the child is still moving at the same speed as at the top. The only difference is the direction of the centripetal acceleration, which is now downwards instead of upwards. The apparent weight can be calculated in the same way as at the top, by subtracting the actual weight, mg, from the total force, mg - ma.
Complete question
an elementary student of mass m=34 kg is swinging on a swing. the length from the top of the swing set to the seat is L=4.7 m. the child is attempting to swing all the way around in a full circle.
-what is the minimum speed in meters per second the child must be moving with at the top of the path in order to make a full circle?
-assuming the child is traveling at the speed found in part a what is their apparent weight in newtons at the top of their path? (at the top, the child is upside-down)
-if the velocity at the very top is the same velocity from part a what is the childs apparent weight in newtons at the very bottoms of the path?