Find the tension in each cord in Fig. E$5.7$ if the weight of the suspended object is $w$.

A man pushes on a piano with mass $180$ kg; it slides at constant velocity down a ramp that is inclined at $19.0°$ above the horizontal floor. Neglect any friction acting on the piano. Calculate the magnitude of the force applied by the man if he pushes parallel to the incline.

A man pushes on a piano with mass $180$ kg; it slides at constant velocity down a ramp that is inclined at $19.0°$ above the horizontal floor. Neglect any friction acting on the piano. Calculate the magnitude of the force applied by the man if he pushes parallel to the floor.

A large wrecking ball is held in place by two light steel cables (Fig. E$5.6$). If the mass m of the wrecking ball is $3620$ kg, what are the (a) tension $T_B$ in the cable that makes an angle of $40°$ with the vertical and (b) the tension $T_A$ in the horizontal cable?

A picture frame hung against a wall is suspended by two wires attached to its upper corners. If the two wires make the same angle with the vertical, what must this angle be if the tension in each wire is equal to $0.75$ of the weight of the frame? (Ignore any friction between the wall and the picture frame.)

A $75.0$-kg wrecking ball hangs from a uniform, heavy-duty chain of mass $26.0$ kg. What is the tension at a point three-fourths of the way up from the bottom of the chain?

A $550$-N physics student stands on a bathroom scale in an elevator that is supported by a cable. The combined mass of student plus elevator is $850$ kg. As the elevator starts moving, the scale reads $450$ N. Find the acceleration of the elevator (magnitude and direction).