6) A child with a weight of 470.0 N grabs onto the end of a rope whose length is 1.80 m. The child swings back and forth, as a pendulum. As the rope swings vertically, the speed of the child is 0.800 m/s. a) What is the acceleration of the child (magnitude and direction), at the moment when the rope is vertical? b) At the moment when the rope is vertical, what force does the rope exert on the child, in order to keep the child hanging onto the rope?

Gibbons, small Asian apes, move by brachiation, swinging below a handhold to move forward to the next handhold. A 9.0 kg gibbon has an arm length (hand to shoulder) of 0.60 m. We can model its motion as that of a point mass swinging at the end of a 0.60-m-long, massless rod. At the lowest point of its swing, the gibbon is moving at 3.5 m/s. What upward force must a branch provide to support the swinging gibbon?

6. A frictionless cart sits on a ramp that is tilted down at an angle of 30.0° from horizontal. The cart is released from rest, with an initial position of * = [0 m] + [0.500 mlj It rolls down the ramp (down and to the right) once it is released, and it's acceleration points down the ramp, parallel to the ramp, with a magnitude of 4.90 m/s². Use a coordinate system where up is +y and to the right is +x. a. What are the x- and y-components of the cart's initial velocity? b. What are the x- and y-components of the cart's acceleration? c. Use your answers to parts a and b to find the cart's position and velocity 1.50 seconds after it is released. Write your answers in unit vector notation.

11.Determine the acceleration a. The masses are: m, = 1 kg, m2 = 2 kg, m3 = 4 kg %3D The coefficient of kinetic friction between mass 1 and the incline is M1 = 0.4 The coefficient of kinetic friction between mass 2 and the flat section is Hz = 0.3 a T1 T2 a Tj m2 T2 m1 H2 a m. H1 30°