1. (a) You shoot a 55 gram dart vertically upwards from a catapult with a spring
ID: 1412413 • Letter: 1
Question
1. (a) You shoot a 55 gram dart vertically upwards from a catapult with a spring constant of 346 N/m. The catapult is initially stretched from the equilibrium point by 36 cm. What is the height above the starting point reached by the dart? Ignore air resistance and give your answer to 2 s.f.
(b) A horizontal spring with a spring constant k = 318 N/m is uncompressed from a length of 2.8 cm back to its unstretched length. Calculate the change in potential energy in Joules to 2 s.f.
(c) A box with an initial velocity of 2.5 m/s is pushed horizontally though a displacement of 2.7 metres by a force of 24.7 Newtons. Non-conservative forces (friction) remove {MC} Joules from the system.What is the net work done on the system?
(d) A force 19.9 acting at a distance 10.9 cm from the centre of rotation of a pulley causes a rotational displacement of 0.50 radians. Calculate the rotational work in Joules, to 3 sf.
Explanation / Answer
A) by energy conservation,
Spring potential energy = gravitational potential enrgy
0.5 kx^2 = mgh
0.5*346*0.36*0.36 = 0.055*9.8* h
h = 0.5*346*0.36*0.36/(0.055*9.8)
= 42 m
B) change in PE = 0 - 0.5*318*0.028*0.028
= -0.12 J
C) Net work done = change in KE
= 24.7*2.7 - MC Joules
D)Work = Torque*radians
= 19.9*0.109*0.50
=1.08 J
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