| Date | May 2016 | Marks available | 2 | Reference code | 16M.2.SL.TZ0.1 |
| Level | Standard level | Paper | Paper 2 | Time zone | Time zone 0 |
| Command term | Determine | Question number | 1 | Adapted from | N/A |
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.
(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.
Describe the motion of the block
(i) from A to B with reference to Newton's first law.
(ii) from B to C with reference to Newton's second law.
On the axes, sketch a graph to show how the displacement of the block varies with time from A to C. (You do not have to put numbers on the axes.)
The spring decompression takes 0.42s. Determine the average force that the spring exerts on the block.
The electric motor is connected to a source of potential difference 120V and draws a current of 6.8A. The motor takes 1.5s to compress the spring.
Estimate the efficiency of the motor.
Markscheme
(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»
Award [1 max] for use of g=10Nkg–1, gives 682 J.
(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.
(i)
no force/friction on the block, hence constant motion/velocity/speed
(ii)
force acts on block OR gravity/component of weight pulls down slope
velocity/speed decreases OR it is slowing down OR it decelerates
Do not allow a bald statement of “N2” or “F = ma” for MP1.
Treat references to energy as neutral.
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
Ignore any attempt to include motion before A.
Gradient of curve must always be less than that of straight line.
\(F\ll = \frac{{\Delta p}}{{\Delta t}}\gg = \frac{{55 \times 4.9}}{{0.42}}\)
F=642≈640N
Allow ECF from (a)(ii).
«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%
Allow ECF from earlier results.
