In a game of tug-of-war, a rope is pulled to the left with a force of 75 N and to the right with a force of 100 N. What is the magnitude and direction of the net external force on the rope?

Waves are used in many practical applications to support work, entertainment, and health. one example is the use of ultrasound imaging to safely track the development of a growing fetus. what is a specific example of a practical application of waves in medicine, entertainment, safety, or other fields? provide a brief explanation of how the properties of waves are useful to that application.

Carbon is allowed to diffuse through a steel plate 15 mm thick. the concentrations of carbon at the two faces are 0.65 and 0.30 kg c/m^3 fe, which are maintained constant. if the preexponential and activation energy are 6.2 x 10-7 m2 /s and 80,000 j/mol, respectively, compute the temperature at which the diffusion flux is 1.43 x 10^-9 kg/m^2 -s.

Find the magnetic field a distance r from the center of a long wire that has radius a and carries a uniform current per unit area j in the positive z direction.