Problem Statement
A particle starts from rest and moves under a constant force F at angle α to the horizontal (on a smooth horizontal surface). Find the velocity and displacement after time t.
Given
F at angle α, m, starts from rest, smooth surface. 2D motion.
Concepts & Formulas
Horizontal: Fx = F cosα → ax = F cosα/m. Vertical (if horizontal plane, ignore gravity component normal to surface): ay = F sinα/m. v = at.
Step-by-Step Solution
Step 1: ax = (F cosα)/m, ay = (F sinα)/m.
Step 2: vx = ax·t = Ft cosα/m, vy = ay·t = Ft sinα/m.
Step 3: v = Ft/m (resultant, since direction is fixed at angle α).
Step 4: Displacement s = ½(F/m)t².
Worked Calculation
v = Ft/m (along direction of F). s = Ft²/(2m).
Boxed Answer
v = Ft/m; s = Ft²/(2m) along direction of F
Physical Interpretation
A constant force produces uniform acceleration regardless of direction. The particle moves in a straight line along the force direction when starting from rest.
Leave a Reply