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Question 19M.3.SL.TZ2.9

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Date May 2019 Marks available [Maximum mark: 5] Reference code 19M.3.SL.TZ2.9
Level SL Paper 3 Time zone TZ2
Command term Calculate, Show that Question number 9 Adapted from N/A
9.
[Maximum mark: 5]
19M.3.SL.TZ2.9

The moment of inertia of a solid sphere is  I = 2 5 m r 2 where m is the mass of the sphere and r is the radius.

(a)

Show that the total kinetic energy Ek of the sphere when it rolls, without slipping, at speed v is  E K = 7 10 m v 2 .

 

[2]

Markscheme

Ek = Ek linear + Ek rotational

OR

E k = 1 2 m v 2 + 1 2 I ω 2   ✔

= 1 2 m v 2 + 1 2 × 2 5 m r 2 × ( v r ) 2  ✔

« = 7 10 m v 2 »

 

Answer is given in the question so check working is correct at each stage.

Examiners report

The derivation of the formula for the total kinetic energy of a rolling ball was well answered.

(b)

A solid sphere of mass 1.5 kg is rolling, without slipping, on a horizontal surface with a speed of 0.50 m s-1. The sphere then rolls, without slipping, down a ramp to reach a horizontal surface that is 45 cm lower.

Calculate the speed of the sphere at the bottom of the ramp.

[3]

Markscheme

Initial  E K = 7 10 × 1.50 × 0.5 2 «=0.26J»  ✔

Final  E K = 0.26 + 1.5 × 9.81 × 0.45  «=6.88J»  ✔

v = « 10 7 × 6.88 1.5 = » 2.56 «m s–1»  ✔

 

Other solution methods are possible.

 

Examiners report

Although there were many correct answers, many candidates forgot to include the initial kinetic energy of the ball at the top of the ramp. The process followed to obtain the answer was too often poorly presented, candidates are encouraged to explain what is being calculated rather than just writing numbers.

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