University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

83

Pages:

5
Author:

Jabin F.

# Projectile Motion in 2-dimensional motion near earth's surface Mostly we deal 3-d motion as two 1-d motion along x & y direction separately EOM in x direction: Fₓ = max => 0 = max => ax = 0 Note: If both upward & downward motion is involved then it is better to use sign convention according to co-ordinate system. EOM in y direction: Fᵧ = may => -mg = may => ay = -g for x direction: sₓ = uₓt + 1/2 at² for y direction: sᵧ = uᵧt + 1/2 ayt² = uᵧt - 1/2 gt² vₓ = uₓ + axt = uₓ + 0t = uₓ cos θ vᵧ = uᵧ + ayt = uᵧ - gt Note: In projectile motion, horizontal component of velocity doesn't change. Equations (1), (2), (3), (4) are basic results for projectile motion. All questions of projectile are solved using these equations. Action: S = ∫Ldt where L = Lagrangian = T - V T = ½m(ẋ² + ẏ²) = ½m(uₓ² + uᵧ²) Put uₓ & uᵧ in terms of t from eq. (1) to (4) V = mgy where y is in terms of t from eq. (1) to (4) Q-54 An object is dropped on a cushion from a height 10 m above it. On being hit, the cushion is depressed by 0.1 m. Assuming that the cushion provides a constant resistive force, the deceleration of the object after hitting the cushion, in terms of acceleration due to gravity g, is: Solution: → velocity of object when reached to cushion h = 10 m v = √(2gh) = √(20g) Since cushion provides a constant resistive force; a = constant v² = u² + 2as 0 = (20g) + 2a(0.1) a = -100g Q. A ball weighting 100 gm released from a height of 5m, bounces perfectly elastically off a plate. The collision time b/w the ball and the plate is 0.58. The avg. force on the plate is approximately. Solution: speed of ball when reached the plate h = 5m : v = √(2gh) = √(10g) elastically bounces: rebound speed = v = √(10g) same avg force due to collision = (p_after collision - p_before collision) / collision time = m(v - (-v)) / 0.5 = m/0.5 * 2√(10g) = 0.1 * 2√(10 * 10) = 4 N net average force = avg. force due to collision + weight = + mg