Working with momentum conservation.

A 82 kg astronaut is space-walking outside the space capsule and is stationary when the tether line breaks. As a means of returning to the capsule, he throws his 3.1 kg wrench at a speed of 13 m/s away from the capsule. At what speed does the astronaut move toward the capsule?

Energy & centripetal force. Small mass slides down a circular surface, loses contact, and travels in free fall to ground impact.

Energy conservation, centripetal acceleration and force, and projectile. A circular pipe whose radius R= 10 m, has a frictionless surface. A small frictionless mass placed on its highest point, slides down to a point where it loses contact, then travels in free fall to impact on the ground. See the diagram in the attachment. a. Find the angle b from vertical to a radius from center to the small mass at the instant it loses contact. b. For an x,y origin at the point where it loses contact, find the x and y coordinates of the impact point on the ground. See diagram on the attachment.

blocks in water

Shown below are six containers that contain various liquids. Blocks of various solids are suspended in the liquids by being hung from a string. All of these blocks are the same size, but they have different masses (labeled as M_b ) since they are made of different materials. All of the containers have the same volume of liquid, but the masses of these liquids vary (labeled M_l ) since the liquids are different. Specific values for the masses of the blocks and the liquids are given in each figure. NOTE: the volume of the blocks is one-fifth the volume of the liquids. Which of the following statements are true about the situations depicted in the figures above? (Give ALL correct answers: ... click for more

Calculating angular acceleration.

The blades in a blender rotate at a rate of 8380 rpm. When the motor is turned off during operation, the blades slow to rest in 3.03 s. What is the angular acceleration, assumed to be constant, as the blades slow down?

Relative velocity with a boat moving on a river. Requires vector polygon solutions.

Relative Velocity Problem Consider a boat on the West bank of a river of width D=1664 meters to be at the origin of an x,y axis system with the 0° direction East along the +x axis. The river water runs South with velocity vector W= 3.9 m/sec at 270°. At coordinates (1200, -390) is a dock on an island. At coordinates (1664, 0) is a cabin. The boat starts at (0,0), pointing to a heading of 0°, with unknown speed B relative to the water. Combined with the current velocity, it moves in a straight line to the dock with actual velocity A, arriving in 100 seconds. Carefully observe the problem attachment, a picture illustrating all given information in Fig. 1. a. Find the magnitude a... click for more