Work, Energy & Power (OCR A Level Physics)

Wind turbines convert the kinetic energy of the wind into electrical energy.

Fig. 18 shows a wind turbine.

Fig. 18

When the wind speed is 8.0 m s⁻¹, the kinetic energy of the air incident at the turbine per second is 1.2 MJ s⁻¹.

 Calculate the mass of the air incident at the turbine per second.

mass per second = ............................................... kg s⁻¹

A group of engineers are investigating the design of wind turbines.

 The maximum input power P from the wind is given by the equation

where A is the area swept out by the rotating blades, t is the density of air and v is the speed of the wind.

 i) Show that the equation is homogeneous with both sides of the equation having the same base units.

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ii) The input power to the wind turbine is 1.2 MW when the wind speed is 8.0 m s⁻¹.

 The density of air is 1.3 kg m⁻³.

 Calculate the length L of the turbine blades.

L = ..................................................... m [2]

iii) A wind farm is required to produce an output power of 50 MW when the average wind speed is 8.0 m s⁻¹. The efficiency of each wind turbine is 42%.

 Calculate the minimum number N of wind turbines required to meet this demand.

N = ......................................................... [2]

Fig. 4.1 shows an arrangement used by a student to determine the acceleration of free fall.

Fig. 4.1

A trolley is attached to a variable mass m by a string which passes over a pulley.

The mass m is released from rest and falls through a fixed height of 0.600 m accelerating the trolley of mass 0.800 kg. When the mass m hits the floor, the trolley then continues to move at a constant velocity v.

This constant velocity v is determined by measuring the time t for the card of length 0.200 m to pass fully through a light gate connected to a timer.

Frictional forces on the trolley and the falling mass m are negligible.

Show that the relationship between v and m is

where g is the acceleration of free fall.

The student records the information from the experiment in a table. The column headings and just the last row for m = 0.600 kg from this table are shown below.

  i) Complete the missing value of v² in the table including the absolute uncertainty.

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ii) Fig. 4.2 shows some of the data points plotted by the student. Plot the missing data for m = 0.600 kg on Fig. 4.2 and draw the straight line of best fit. 

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Fig. 4.2

i) Use the equation given in (a) to show that the gradient of the graph of v² against  is equal to 1.20 g.

[1]

ii) Assume that the best-fit straight line through the data points gives 9.5 m s^–2 for the experimental value of g. Draw a worst-fit line through the data points on Fig. 4.2 and determine the absolute uncertainty in the value for g.

absolute uncertainty = ± .................... m s⁻² [4]

It is suspected that the card on the trolley did not pass at right angles through the light beam.

Discuss, without doing any calculations, the effect this may have on the experimental value for the acceleration of free fall g.