University:
Angelo State University
Course:
ENGR 2302 | Engineering Mechanics - Dynamics
Academic year:

2024
Views:

499

Pages:

5
Author:

Cyncuncewc3b4

SOLUTIONS TO HOMEWORK PROBLEMS HW#2 12-67, 75, 85, 93, 98 Problem 12-67 The velocity of a particle is given by v = [at²i + bt³j + (ct + d)k]. If the particle is at the origin when t = 0, determine the magnitude of the particle's acceleration when t = t₁. Also, what is the x, y, z coordinate position of the particle at this instant? Given: a = 16 m/s³ b = 4 m/s⁴ c = 5 m/s² d = 2 m/s t₁ = 2 s Solution: Acceleration a_x = 2at₁ = 64 m/s² a_y = 3bt₁² = 48 m/s² a_z = c = 5 m/s² a_mag = √(a_x² + a_y² + a_z²) = 80.2 m/s² Position x = (a/3)t₁³ = 42.667 m y = (b/4)t₁⁴ = 16 m z = (c/2)t₁² + dt₁ = 14 m Problem 12-75 The path of a particle is defined by y² = 4kx, and the component of velocity along the y axis is v_y = ct, where both k and c are constants. Determine the x and y components of acceleration. Solution: y² = 4kx 2y * v_y = 4k * v_x 2y * v_y + 2y * a_y = 4k * a_x v_y = ct a_y = c 2(ct)² + 2yc = 4k * a_x a_x = (c/2k)(ct² + y)