Question
A company designs a spring system for loading ice blocks onto a truck. The ice block is placed in a holder H in front of the spring and an electric motor compresses the spring by pushing H to the left. When the spring is released the ice block is accelerated towards a
ramp ABC. When the spring is fully decompressed, the ice block loses contact with the spring at A. The mass of the ice block is 55 kg.
Assume that the surface of the ramp is frictionless and that the masses of the spring and the holder are negligible compared to the mass of the ice block.
a. (i) The block arrives at C with a speed of 0.90ms−1. Show that the elastic energy stored in the spring is 670J.
(ii) Calculate the speed of the block at A. [4]
(i) from A to B with reference to Newton’s first law.
(ii) from B to C with reference to Newton’s second law. [3]
[2]
Estimate the efficiency of the motor. [2]
Answer/Explanation
Ans:
a. (i)
\(\ll {E_{{\rm{el}}}}{\rm{ = }}\gg \frac{1}{2}m{v^{\rm{2}}} + mgh\)
OR
«Eel=»EP+EK
\(\ll {E_{{\rm{el}}}}{\rm{ = }}\gg \frac{1}{2} \times {\rm{55}} \times {\rm{0.9}}{{\rm{0}}^{\rm{2}}}{\rm{ + 55}} \times {\rm{9.8}} \times {\rm{1.2}}\)
OR
669 J
«Eel = 669 ≈ 670J».
(ii)
\(\frac{1}{2} \times {\rm{55}} \times {v^{\rm{2}}} = 670{\rm{J}}\)
\(v = \ll \sqrt {\frac{{2 \times 670}}{{55}} = } \gg 4.9{\rm{m}}{{\rm{s}}^{ – 1}}\)
If 682J used, answer is 5.0ms–1.
b.(i)
no force/friction on the block, hence constant motion/velocity/speed
b (ii)
force acts on block OR gravity/component of weight pulls down slope
velocity/speed decreases OR it is slowing down OR it decelerates
straight line through origin for at least one-third of the total length of time axis covered by candidate line
followed by curve with decreasing positive gradient
F=642≈640N
«energy supplied by motor =» 120 × 6.8 × 1.5 or 1224 J
OR
«power supplied by motor =» 120 × 6.8 or 816 W
e = 0.55 or 0.547 or 55% or 54.7%