...descending and ascending on inclined planes : the force of gravity on the plane being represented by g sin. a, where a is the 'inclination of the plane to the horizon. In Dr. Hutton's Tracts there is given a problem for determining the height ascended by a ball when...

...and AP ; then R has received no virtual velocity, and that of P is - AL, that of W is AK. Now AK= AA' sin a, where a is the inclination of the plane to the horizon, and AL = AA' cos 6, therefore W.AK - P.AL = ( TFsin a - P cos 0) AA', STATICS. [Art. 85 85. It holds...

...following examples can be solved by means of the principle laid down in Art. 1 10. Ex. 628. — If a body slides down a smooth inclined plane, show that the accelerating force equals g sin o, where a is the inclination of the plane to the horizon j if the plane is rough show that the accelerating...

...The following Examples can be solved by means of the principle laid down in Art. 118. Ex. 630. — If a body slides down a smooth inclined plane, show that...is rough, show that the accelerating force equals - (a—v) wnere ,* is tne limiting angle of resistance. cos <p [In the case of a smooth plane the pressure...

...The following Examples can be solved by means of the principle laid down in Art. 118. Ex. 630. — If a body slides down a smooth inclined plane, show that...is rough, show that the accelerating force equals sm (a—t>) whcre Q ;s the limiting angle of resistance, cos (ft [In the case of a smooth plane the...

...The following Examples can be solved by means of the principle laid down in Art. 118. Ex. 674. — If a body slides down a smooth inclined plane, show that the accelerating force equals g sin a, where o is the inclination of the plane to the horizon ; if the plane is rough, show that the accelerating...

...in Art. 118. Ex. 687. — If a body slides down a smooth inclined plane, show that the acceleration equals g sin a, where a is the inclination of the...the horizon ; if the plane is rough, show that the acceleration equals sin (<*—<p> wiiere ^ ;s the lim;ting angle of resistance, cos <f> [In the case...

...friction changes at a point of the string, the natural distance of which from the upper end is tan a where a is the inclination of the plane to the horizon. 24. A heavy elastic cord is passed through a number of fixed smooth rings. Shew that in the position...

...q, shew that the particle will just come to rest at the foot of the plane if /*• = - — — tan a, where a is the inclination of the plane to the horizon. 2. A point moving with uniform acceleration /in the direction of motion describes er feet in T seconds,...

...roll. The problem then n becomes the same as that discussed in Art. 133. We have, therefore, = = f tan a, where a is the inclination of the plane to the horizon. If then ;' tan a be not greater than ,u, the solution given in the article referral to is the correct...