Motion on a Rough Inclined Plane A trolley of mass 0.5 kg is released from rest at a point O on a rough runway inclined at 30o to the horizontal. It slides down the runway and the velocity-time graph is given below. Assume g = 10 m s-2 Determine the friction and normal V / m s-1 reaction on the trolley. h roug 1.6 lley tro O 1.2 0.8 0.4 t/s 0 0.2 0.4 3o horizontal A trolley of mass 0.5 kg is released from rest at a point O on a rough runway inclined at 30o to the horizontal. It slides down the runway and the velocity-time graph is given below. Assume g = 10 m s-2 From the velocity-time graph the acceleration of the trolley is 4 m s-2. The acceleration vector V / m s-1 points down-slope. h roug 1.6 lley tro O 1.2 0.8 0.4 t/s 0 0.2 0.4 3o horizontal In the direction perpendicular to the inclined plane, there is NO motion. Normal Reaction R = mg cos = 0.5 1 cos 30o = 4.33 N h R rou g ) -2 i on s fr ict 4m Q( a= s in mg c os mg 3 horizontal In the direction along the inclined plane, there is MOTION. Apply F = ma mg sin - Q = ma Q = mg sin - ma Q = 0.5 1 sin 30o - .5 4 h = 2.5 - 2. R rou g ) .5N -2 i on s fr ict 4m Q( a= s in mg c os mg 3 horizontal At a certain inclination of the runway, the trolley can move down- slope with uniform velocity after given a push. Find the value for this to occur. R -2 y m s velocit h Q = .5N roug a = 0 iform n ) n fo r u sin Q (f rictio The forces along the mg inclined should be balanced mg cos horizontal mg sin = Q 0.5 1 sin = .5 = 5.74o At = 5.74o , the runway is friction-compensated. R -2 Q = .5N y m s velocit h roug mg sin 5.74o = 0.5 N a = 0 iform n ) n fo r u sin Q (f rictio mg mg cos horizontal At this inclination, the friction is balanced by the down-slope component of the weight. In doing experiments concerning a trolley moving on a horizontal runway, friction affects the results of the experiment. By sloping the runway at a certain angle (usually very small) with the horizontal, the effect of friction can be canceled. The runway is said to be friction-compensated. To find the inclination of the runway for friction compensation, the runway can be slightly inclined and then a trolley on it is given a push. If the trolley moves down the runway with uniform velocity, it is friction-compensated. Otherwise the inclination is adjusted again. The velocity of the trolley can be studied using a ticker-tape timer or a motion sensor.