A mountain climber swings a grappling hook (m=0.75 kg) at the end of a 0.6 m long rope in a vertical circle with a speed of 11 m/s.  Determine the tension in the rope when the hook is at the top of the circle.

In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for the rockets position measured from the center of the Earth is given by y(t)=(R3/2+3g2Rt)2/3j where R is the radius of the Earth (6.38 106 m) and g is the constant acceleration of an object in free fall near the Earths surface (9.81 m/s2). a. Derive expressions for vy(t) and ay(t). b. Plot y(t), vy(t), and ay(t). (A spreadsheet program would be helpful.) c. When will the rocket be at y=4R? d. What are vy and ay when y=4R?

A ball of mass m = 0.275 kg swings in a vertical circular path on a string L = 0.850 in long as in Figure P6.31. (a) What are the forces acting on the ball at any point on the path? (b) Draw force diagrams for the ball when it is at the bottom of the circle and when it is at the top. (c) If its speed is 5.20 m/s at the top of the circle, what is the tension in the string there? (d) If the string breaks when its tension exceeds 22.5 N, what is the maximum speed the ball can have at the bottom before that happens? Figure P6.31

A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 18.4 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 97.0 m), the block swings toward the outside of the curve. Then the string makes an angle 8 with the vertical. Find 0. Number i Units To center of curve