Year 2 Mechanics Revision Christmas Theme

If a = (4t + 5)i + 6tj m/s² is the acceleration of Santa's sleigh and the sleigh is initially at rest, what is its velocity when t = 4 as Santa delivers presents?

• 15i - 3j

• 26i + 24j

• 52i + 48j

• 15i + 25j

Answer explanation

v(t) = ds/dt = 3t² - 6t

v(5) = 3×5² - 6×5

= 45 m/s

In a Christmas movie scene, Santa is setting up his sleigh at point O. An elf pulls the sleigh with a force of 3 N at an angle, 5 m away from O, while a reindeer tugs downward with a force of 8 N, 7 m away from O. Find the magnitude of the total moment of this festive system of forces, in Nm, about the point O.

Answer explanation

Total moment, remembering that clockwise moments are negative is

3×5 - 7×8

= -41 Nm, so magnitude is 41

In Santa's workshop, a uniform candy cane AB of mass 10 kg is freely hinged at A and is kept horizontal by a festive ribbon from B to a hook vertically above A. The ribbon makes an angle of 30° with the candy cane.

Find the tension, in newtons, in the ribbon.

Take g as 9.8 m/s²

Answer explanation

A Christmas garland, 8 metres long, has ornaments of 1kg, 3kg and 2kg placed 2m, 4m and 8m respectively from one end, O.

What is the distance of the centre of mass of the garland and ornaments from O, in metres?

Answer explanation

In a Christmas movie set, a heavy rod AB (representing Santa's sleigh rail) with a mass of 25kg and length 2.4m is hinged at A to a point on a vertical wall (the North Pole workshop). It is kept horizontal by a festive chain attached to B and a point 1.5m vertically above A (where a Christmas star is hung). The sleigh rail carries an additional present weighing 10kg, placed 1.8m from A.

Find the tension, in newtons, in the festive chain, correct to 3 s.f.

Answer explanation

Santa's sleigh is delivering presents, and its velocity is modelled by

v = (3t²i + 10tj) m/s.

Given that r = (4i - 4j)m when t = 0 (just as Santa leaves the North Pole).

Find the distance of the sleigh, in metres, from the origin (the North Pole) when t = 2.

Santa’s sleigh, loaded with gifts and having a mass of 30 kg, starts from rest and is pulled by reindeer with a force of 50 N against a resistance of 25 N for a distance of 15 m as it glides over the snowy rooftop.

How fast is the sleigh then going in m/s?