Dymamics Second Law and Dynamics

Unbalanced Forces If forces are NOT in equilibrium, then the are NOT Balanced (NOT equal and opposite). Instead these forces are considered unbalanced. When forces are unbalanced the net force will have a non-zero value, which results in acceleration according to Newton’s 2nd law. The method of solution for unbalanced force problems is the same as it is for equilibrium problems, with one exception: During the “solve” step, substitute ma instead of zero in place of the sum of force vectors, ΣF .

Example 1 A 10 kg mass is pulled along a frictionless surface by a rope exerting 20 N of force. Determine the magnitude of acceleration. 10 kg Assess: Moving in the x-direction, accelerating, ΣFx = ma Stationary in the y-direction, equilibrium, ΣFy = 0 Diagram: Sum forces: Solve: T N Fg The x- and y-directions are mathematically independent. Solve for either or both as problems dictate.

20 N 10 kg Example 2 A 10 kg mass, initially at rest, is pulled by a rope with 20 N of tension directed 37o. Assess: Moving in the x-direction, accelerating, ΣFx = ma Stationary in the y-direction, equilibrium, ΣFy = 0 Diagram: Sum forces: Solve: +Ty +Tx +N −Fg T N Fg T