Dynamics L6 Worked example 1 (ENGR5004)

Dynamics L6 Worked example 1TutorialOld spec ENGR2162:210 min

ENGR216 Dynamics L6 worked example 1 (slides 12-14) official answers

A 10 kg block on a smooth horizontal surface ( $\mu_k = 0$ ) is pushed by a constant force $F = 500$ N whose line of action slopes downwards towards the block with a 3-4-5 slope (4 horizontal, towards the spring; 3 vertical, downwards). A spring of stiffness $k = 500$ N/m is mounted between the block and a wall ahead of it. When $s = 0$ the block is at rest and the spring is uncompressed; $s$ is the block's displacement towards the wall. Take $g = 9.81$ m/s $^2$ .

10 kg block pushed by F = 500 N along a 3-4-5 slope (down and to the right) towards a spring k = 500 N/m attached to a wall; s is the block displacement.

Formulas you may need

Newton's second law: $\sum F_x = m a_x$ , $\sum F_y = m a_y$ (learn this)
Linear spring: $F_s = k s$ (learn this)
$a\,ds = v\,dv$ when $a = a(s)$ (learn this)

(a)
Draw the free-body and kinetic diagrams of the block and find the normal reaction and $a(s)$ .
N =N
(b)
Find the velocity of the block when $s = 0.5$ m.
v =m/s