A sphere of mass 4.9 × 104 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes a constant angle of 22° with the vertical. Find (a) the magnitude of that push and (b) the tension in the cord. (a) Number i 19.4 Units N (b) Number i 51.79 Units

A laboratory on the concept of static equilibrium uses an apparatus called a force table. The force table consists of a round, level platform marked in degree increments about its circumference. In the center of the table sits a massless ring, to which three strings are tied. Each string is strung over a separate pulley clamped to the edge of the platform, and then tied to a freely-hanging mass, so that each string is under tension and the ring is suspended parallel to the table surface. A mass of ?1 =0.145 kg is located at ?1 =26.5∘ , and a second mass of ?2 =0.227 kg is located at ?2=283∘ . Calculate the mass ?3 and the angular position ?3 (in degrees) that will balance the system and hold the ring stationary over the center of the platform.

A pulley is attached to one end of a rough plank, which makes an angle of 34° with the horizontal. A box is held at rest on the plank by a string that is attached to the box and passes over the pulley. A bucket of water is attached to the other end of the string and hangs freely. The coefficient of static friction between the plank and the box is 0.8. The box remains at rest but is on the point of slipping up the plank. The bucket of water has mass 7.5 kg. pulley box bucket of water 34° Model the box and the bucket of water as particles, the string as a model string and the pulley as a model pulley. (a) By considering the forces acting on the bucket of water, find the magnitude of the tension in the string (in newtons) in terms of g and the magnitude of the acceleration due to gravity (in ms-2). (b) State the four forces that act on the box and draw a force diagram showing them, including the angles that show their directions. (c) Take the unit vector i to be in the direction up the…