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Space, time and motion · Question 9

Space, time and motion · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
demanding
Marks
12
Topics
1
Answer
Complete
Cyclist riding at constant speed up a slope4.0°total mass 78 kg5.5 m s⁻¹25 Nlengths not to scale
Figure 4Side view, drawn not to scale. A road climbs to the right from level ground, and the angle between the road and a dashed horizontal line drawn from the foot of the slope is marked 4.0°. The cyclist and bicycle are drawn as one wheeled body on the road, labelled total mass 78 kg. An arrow from the front of the body points up the slope and is labelled 5.5 m s⁻¹; a second arrow from the rear points down the slope and is labelled 25 N.
structured12 marks

A cyclist and her bicycle have a combined mass of 78 kg. She rides up a straight road inclined at 4.0° to the horizontal at a constant speed of 5.5 m s⁻¹. The total resistive force opposing her motion is 25 N.

  1. (a)

    Define Define power.

    1 mark
  2. (b)

    Determine Determine the component of the total weight acting down the slope.

    2 marks
  3. (c)

    Calculate Calculate the useful power output of the cyclist.

    3 marks
  4. (d)

    Determine The cyclist's body converts chemical energy to mechanical work with an efficiency of 22%. Determine the rate at which she uses chemical energy.

    2 marks
  5. (e)

    Discuss At the top of the hill the cyclist stops pedalling and freewheels down the other side, which has the same gradient. Discuss whether she reaches a constant speed, and what determines its value.

    4 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: the rate at which work is done, or the rate at which energy is transferred component = mg sin θ = 78 × 9.81 × sin 4.0° Evaluating mg sin 4.0° gives a downslope weight component of 53 N.
01

(a)

1 mark

Define Define power.

How to approach it

Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.

  1. 1

    the rate at which work is done, or the rate at which energy is transferred

02

(b)

2 marks

Determine Determine the component of the total weight acting down the slope.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    component = mg sin θ = 78 × 9.81 × sin 4.0°

  2. 2

    Evaluating mg sin 4.0° gives a downslope weight component of 53 N.

03

(c)

3 marks

Calculate Calculate the useful power output of the cyclist.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    at constant speed the driving force balances the weight component and the resistive force: F = 53 + 25 = 78 N

  2. 2

    P = Fv = 78 × 5.5

  3. 3

    P = 4.3 × 10² W

04

(d)

2 marks

Determine The cyclist's body converts chemical energy to mechanical work with an efficiency of 22%. Determine the rate at which she uses chemical energy.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    input power = 429 / 0.22

  2. 2

    = 1.9 × 10³ W

05

(e)

4 marks

Discuss At the top of the hill the cyclist stops pedalling and freewheels down the other side, which has the same gradient. Discuss whether she reaches a constant speed, and what determines its value.

How to approach it

Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.

  1. 1

    on the way down, the component of weight along the slope now acts in the direction of motion and accelerates her

  2. 2

    the resistive force increases with speed, mainly because air resistance rises steeply with speed

  3. 3

    she reaches a constant speed when the resistive force has grown to equal the 53 N component of weight down the slope

  4. 4

    the value of that speed is set by how quickly the resistive force grows with speed — by her frontal area, her posture and the air density, not by her mass alone

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