IB DP Physics Topic 2: Mechanics Question Bank SL Paper 3

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Question

A wheel of mass 0.25 kg consists of a cylinder mounted on a central shaft. The shaft has a radius of 1.2 cm and the cylinder has a radius of 4.0 cm. The shaft rests on two rails with the cylinder able to spin freely between the rails.

The stationary wheel is released from rest and rolls down a slope with the shaft rolling on the rails without slipping from point A to point B.

The wheel leaves the rails at point B and travels along the flat track to point C. For a short time the wheel slips and a frictional force F exists on the edge of the wheel as shown.

a.i.The moment of inertia of the wheel is 1.3 × 10^–4 kg m². Outline what is meant by the moment of inertia.[1]

a.ii.In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s^–1 after its displacement.[3]

a.iii.Determine the angular velocity of the wheel at B.[1]

b.i.Describe the effect of F on the linear speed of the wheel.[2]

b.iiDescribe the effect of F on the angular speed of the wheel.[2]

▶️Answer/Explanation

Markscheme

a.i.

an object’s resistance to change in rotational motion

equivalent of mass in rotational equations

OWTTE

[1 mark]

a.ii.

ΔKE + Δrotational KE = ΔGPE

$\frac{1}{2}$mv² + $\frac{1}{2}$I$\frac{{{v^2}}}{{{r^2}}}$ = mgh

$\frac{1}{2}$ × 0.250 × v² + $\frac{1}{2}$ × 1.3 × 10^–4 × $\frac{{{v^2}}}{{1.44 \times {{10}^{ – 4}}}}$ = 0.250 × 9.81 × 0.36

v = 1.2 «m s^–1»

[3 marks]

a.iii.

ω «= $\frac{{1.2}}{{0.012}}$» = 100 «rad s^–1»

[1 mark]

b.i.

force in direction of motion

so linear speed increases

[2 marks]

b.ii

force gives rise to anticlockwise/opposing torque on

wheel ✓ so angular speed decreases ✓

OWTTE

[2 marks]

Question

A uniform ladder of weight 50.0 N and length 4.00 m is placed against a frictionless wall making an angle of 60.0° with the ground.

a. Outline why the normal force acting on the ladder at the point of contact with the wall is equal to the frictional force F between the ladder and the ground. [1]

b. Calculate F. [2]

c. The coefficient of friction between the ladder and the ground is 0.400. Determine whether the ladder will slip. [2]

▶️Answer/Explanation

Ans:

a. «translational equilibrium demands that the» resultant force in the horizontal direction must be zero✔

«hence N_W = F»

Equality of forces is given, look for reason why.

«clockwise moments = anticlockwise moments»

50 × 2cos 60 = N_W × 4sin 60 ✔

« $N_{W} = F = \frac{50 \times 2 \cos 60}{4 \sin 60}$ »

F = 14.4«N» ✔

maximum friction force = «0.4 × 50N» = 20«N» ✔

14.4 < 20 AND so will not slip ✔