University of Wisconsin Green Bay

A moving company needs to lift a 700 lb. (320kg) piano to the top floor of an apartment building. They set up a rope and pulley system on the balcony of the upper story apartment, and pull the piano up. If the piano initially has an acceleration of 0.45 m/s2, what is the tension in the rope during that period of time?

  • In this problem, you are asked to relate motion (the acceleration of the piano) to force (tension). Force and motion of a single object are always related through Newton's Second Law, so this is a force or 2nd Law problem.

  • Tension Tension Tension Tension Tension
  • Object on a rope

    The key equation for any problem that relates forces and motion is Newton's Second Law. Regardless of what quantity you are asked to find, begin with the Second Law. If additional information is needed, it will become apparent as you proceed.

  • Solve
    mg mg - (9.8 m/s2) y (0.45 m/s2) T T y y 3100 N 140 N 3200 N
  • Solve

    In this problem, the rope puts an upward force on the piano. The force by the rope needs to be strong enough to both support the piano against the force of gravity (3100 N) and to give it an upward acceleration. So tension needs to be greater than 3100 N.