Question 1a

Marks: 4

A sun bather is supported in water by a floating sun bed.

sl-sq-2-2-hard-q1a

(a)

Draw and label vectors representing the forces acting on the sun bed.

[4]

Key Concepts

Vectors
Free-Body Diagrams

Question 1b

Marks: 6

The sunbather has incredible core strength and balance.

They stand upright at one end of the sun bed and begin to walk forwards at a constant velocity to the right.

sl-sq-2-2-hard--q1b

(b)

(i)

Describe the magnitudes and directions of the forces acting between the sunbather and the sun bed

[4]

(ii)

Hence, explain the consequent motion of the sun bed.

[2]

Key Concepts

Applying Newton’s Laws of Motion
Newton’s Third Law

Question 1c

Marks: 2

The sun bed and sunbather may be treated as a single, isolated system.

(c)

(i)

Explain how the sun bed and sunbather may be considered as a 'single' system

[1]

(ii)

Explain how the single system may be considered as 'isolated'.

[1]

Key Concepts

Applying Newton’s Laws of Motion

Question 1d

Marks: 3

Treating the sun bed and sunbather as a single, isolated system enables quantitative predictions about its centre of mass.

(d)

(i)

State and explain the change in position of the isolated system's centre of mass as the sun bather walks along it

[2]

(ii)

Describe how the motion of the sun bed would change if it had a much larger mass.

[1]

Key Concepts

Applying Newton’s Laws of Motion

Question 2a

Marks: 2

(a)

Describe the microscopic origin of static friction between two objects.

[2]

Key Concepts

Friction

Question 2b

Marks: 3

(b)

Compare and contrast the static force of friction and the dynamic force of friction.

[3]

Key Concepts

Friction

Question 2c

Marks: 3

A block of mass 2.5 kg is at rest on a rough inclined plane. The block just begins to slip down the plane when the angle of inclination is 35°.

(c)

Calculate the coefficient of static friction between the block and the inclined plane.

You may use the following result:

\tan θ = \frac{\sin θ}{\cos θ}

[3]

Key Concepts

Friction
Free-Body Diagrams

Question 2d

Marks: 3

The angle of inclination is increased to 40°.

(d)

Calculate the force that must be applied to the block to move it up the plane with an acceleration of 1.5 m s^–2.

Use the following data:

μ_d = 0.30

[3]

Question 3a

Marks: 3

A ball travels in a circular path on the inside surface of a bowl.

sl-sq-2-2-hard-q3

The normal reaction force N makes an angle φ to the plane of the ball's path. Ignore the effects of friction.

(a)

On the free-body diagram below, construct an arrow to represent the weight of the ball.

[3]

Key Concepts

Free-Body Diagrams
Vectors

Question 3b

Marks: 2

(b)

Determine an equation for the resultant force acting on the ball in terms of its mass m and the angle to its plane of orbit φ.

You may use the result:

\tan ϕ = \frac{\sin ϕ}{\cos ϕ}

[2]

Key Concepts

Applying Newton’s Laws of Motion

Question 3c

Marks: 3

The radius of the ball's orbit decreases.

(c)

Explain how the effects of friction are related to the decreasing orbital radius.

[3]

Key Concepts

Friction

Question 3d

Marks: 3

(d)

Outline if the ball could travel along a horizontal circular path with an orbital radius equal to the maximum radius of the bowl. Ignore the effects of friction in your answer.

[3]

Question 4a

Marks: 2

A woman stands in an elevator and measures the weight of a fish attached to a spring scale. The scale reads 40 N when the elevator is stationary.

sl-sq-2-2-hard-q4a

(a)

Sketch the reading on the spring scale as the lift gently accelerates upward.

[2]

Key Concepts

Applying Newton’s Laws of Motion

Question 4b

Marks: 2

As the elevator continues moving upwards, it gently decelerates to a standstill.

(b)

Draw and label a free-body force diagram for the fish as the elevator gently decelerates.

[2]

Key Concepts

Applying Newton’s Laws of Motion

Question 4c

Marks: 2

The rope that attaches the spring scale to the ceiling of the elevator suddenly snaps. The spring scale and the fish are momentarily in free-fall – but the observer manages to take a reading from the scale it falls.

(c)

State and explain the reading on the spring scale as it falls.

[2]

Key Concepts

Applying Newton’s Laws of Motion

Question 4d

Marks: 3

(d)

Sketch the variation of the contact force on the observer's feet as the elevator decelerates to rest on the axes provided.

The magnitude of the observers weight, mg, is included as a dashed line, for reference.

[3]

Key Concepts

Applying Newton’s Laws of Motion

Question 5a

Marks: 2

Two blocks of mass 4.5 kg and 6.0 kg are joined by a string and rest on a smooth horizontal table. A force F of 100 N is applied to one of the blocks.

sl-sq-2-2-hard-q5a

(a)

Calculate

(i)

The acceleration of the blocks

[1]

(ii)

The tension in the string.

[1]

Key Concepts

Applying Newton’s Laws of Motion

Question 5b

Marks: 3

The 4.5 kg block is now placed on top of the 6.0 kg block. The coeffecient of static friction between them is 0.40.

(b)

Calculate the maximum horizontal force F that can be applied to the bottom block that would result in both blocks moving together without slipping.

[3]

Key Concepts

Applying Newton’s Laws of Motion

Question 5c

Marks: 4

The two blocks are now attached by a light inextensible string that passes over a smooth pulley. They are held stationary and suddenly released.

sl-sq-2-2-hard-q5c

(c)

Determine the acceleration of each block and the tension in the string.

[4]

Key Concepts

Applying Newton’s Laws of Motion

Question 5d

Marks: 2

The string attaching the blocks over the pulley in part (c) suddenly snaps.

(d)

Describe and explain the subsequent motion of the block of mass 4.5 kg. (Assume it was moving upward at the instant the string snapped).

[2]

Key Concepts

Applying Newton’s Laws of Motion

DP IB Physics: SL

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