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Glancing Stones at Naseby

Momentum and collisions

At an indoor curling rink in Naseby, a moving stone A strikes a stationary stone B a glancing blow. Both stones have mass m=19.0 kgm = 19.0\ \text{kg}. Just before the collision A moves at u=2.40 m s−1u = 2.40\ \text{m s}^{-1} along the xx-axis. A high-speed camera shows that just after the collision A moves at vA=1.10 m s−1v_A = 1.10\ \text{m s}^{-1} in a direction 62.0∘62.0^\circ to the +x+x-axis (on the +y+y side). Speeds are measured to ±0.005 m s−1\pm 0.005\ \text{m s}^{-1} and angles to ±0.5∘\pm 0.5^\circ. Treat the stones as not spinning before the collision, and ignore friction with the ice during the brief collision.

(a)

show that2 marks
Show that if a collision between two equal masses, one initially at rest, is perfectly elastic, the two stones move off at 90∘90^\circ to each other.

(b)

calculate2 marks
Use conservation of momentum to calculate the velocity (magnitude and direction) of stone B just after the collision.

(c)

calculate2 marks
Calculate the kinetic energy before and after the collision, and the percentage lost. Comment on whether this is consistent with the angle between the stones' paths.

(d)

discuss2 marks
A student concludes that 'the collision definitely lost energy, so it was inelastic'. Using the stated measurement uncertainties, discuss whether the data support this conclusion, and suggest where any energy that was lost might have gone.

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