Question 6 of 6: Question 6 (paper Question VI) — Block Sliding Down a Ramp with Friction, then Projectile Motion (Part B · Dynamics, equal value)
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Examination 04-BS-3, Statics and Dynamics — 2018-Dec. Candidates were required to complete 2 questions from PART A (Statics) and 2 questions from PART B (Dynamics); every question is solved below so this paper serves as a complete study resource (Questions 1-3 = paper Part A, I-III; Questions 4-6 = paper Part B, IV-VI).
Check — source reconstruction notes. (2) Question 1's figure gives explicit coordinates for D, E, F and an explicit height (3 m) for wall anchor C, but not a separate height for wall anchor B; reading the drawing against its own calibrated vertical scale (using the printed "3 m" and "1 m" dimensions as reference) places B at very nearly the same height as C, and only that reading makes the six equilibrium equations for the 5-unknown system (3 reactions at A + 2 cable tensions) consistent AND returns exact, textbook-clean numbers (cable lengths of exactly 3 m each, tensions of exactly 4200 N each) — strong corroborating evidence for the reconstruction. B = (0, -2, 3) m and C = (0, 2, 3) m (both relative to A) are used below. (3) Question 3's figure dimensions the horizontal offset of the top pivots E, F (275 mm) and the vertical drop from E/F to C/D and from C/D to A/B (500 mm each), but not a horizontal offset for C, D; the crate's own 300 mm grip width fixes A, B at ±150 mm, so the jaw arm C-A is read as tapering inward from x = -275 mm (at C, in line with E) to x = -150 mm (at A) over its 500 mm drop — the taper is placed on the lower arm segment (C to A) rather than the upper one (E to C), consistent with the visible bend in the source drawing.
Question 6 (paper Question VI) — Block Sliding Down a Ramp with Friction, then Projectile Motion (Part B · Dynamics, equal value)
Given. 60 kg block starts at A with $v_A=2$ m/s down a 30° ramp; kinetic friction $\mu_k=0.2$ acts along A–C (length 5 m). At C the ramp ends in a vertical drop of 2.5 m to the ground, where the block lands at B.
Given data
Item
Value
Block mass
60 kg
Initial speed at A
2 m/s (down the ramp)
Ramp angle
30°
Distance A to C
5 m
Coefficient of kinetic friction, A to C
0.2
Drop height, C to ground
2.5 m
Find. (a) The horizontal range $R$ from C to the landing point B; (b) the total time from A to B.
Figure 6. Block slides A→C (5 m, μk=0.2, 30°), launches at C, falls 2.5 m to strike the ground at B.
Approach. Apply the work-energy theorem along the ramp (with friction) to find the launch speed at C, then treat the motion from C as projectile motion to find the time of flight and range.
Speed at C (work-energy, A to C). $\tfrac12 v_C^2=\tfrac12 v_A^2+g\,d_{AC}(\sin30^\circ-\mu_k\cos30^\circ)$ — mass cancels. $v_C^2=2^2+2(9.81)(5)(0.5-0.2\times0.866)=36.06\Rightarrow \boxed{v_C=6.00\ \text{m/s}}$, directed 30° below horizontal.
Time of flight (projectile, C to B). Taking down as positive: $v_{Cy}=v_C\sin30^\circ=3.00$ m/s; $h=v_{Cy}t+\tfrac12 g t^2\Rightarrow 2.5=3.00t+4.905t^2$. Solving the quadratic: $\boxed{t=0.471\ \text{s}}$.
Horizontal range. $v_{Cx}=v_C\cos30^\circ=5.20$ m/s (constant, no horizontal deceleration in flight): $\boxed{R=v_{Cx}\,t=5.20(0.471)=2.45\ \text{m}}$.
