IAL 2018 mechanics - Distinguish between scalar and vector quantities

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Last updated: January 1, 2024

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Question

Answer

The diagrams below show the velocity of an object before and after a force is applied. The magnitude of the velocity did not change. Which of the following arrows represents the direction of the change in velocity?

iia) An aluminium sphere collides head-on with a stationary steel sphere. The two spheres move off separately after the collision. State the principle of conservation of momentum.

The total momentum before = the total momentum after. Provided no external force acts on the system.

iib) The aluminium sphere has an initial velocity of 10 m/s. Immediately after the collision the velocity of the steel sphere is 5 m/s. Calculate the velocity v of the aluminium sphere immediately after the collision. Mass of aluminium sphere = 2.7 kg Mass of steel sphere = 7.9 kg

P = mv 2.7 x 10 = (2.7 x v) + (7.9 x 5) V = (27 - 39.5) / 2.7 = -4.63 m/s V = -4.6 m/s

Quantities in physics are classified as either vectors or scalars. Which of the following units could only be used for a scalar quantity? A - ms^-1 B - ms^-2 C - kg ms^-2 D - kg m^-3

ia) P and Q are identical spheres. Sphere P moves along a smooth horizontal surface and collides with sphere Q, which is initially stationary. After the collision: -sphere P moves off with a momentum of 0.096 kg m/s in a direction of 15 degrees to its initial direction. -sphere Q moves off with a momentum of 0.14 kg m/s in a direction of 10 degrees. Use a scaled vector diagram to show that the magnitude of the total momentum of spheres P and Q after the collision is about 0.2 kg m/s.

-construction of correct vector diagram, parallelogram or triangle, with all 3 directions and 0.096 kg m/s and 0.14 kg m/s labelled -momenta correctly scaled (ratio lengths 0.14 to 0.096 rounds to between 1.40 and 1.50) -horizontal resultant (to within a slope of 1 small square) -total momentum = 0.22 to 0.24 kg m/s

ib) State the principle of conservation of linear momentum

The total momentum before collision = the total momentum after collision. Provided no external forces act on the system.

ic) Calculate the initial velocity of sphere P. Mass of sphere P = 0.12 kg

P = mv 0.23 = 0.12 x v V = 1.92 m/s V = 1.9 m/s

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