2007 physics semester test

of 6

MASSEY UNIVERSITY Institute of Fundamental Sciences

Physics

124.111 PHYSICS FOR LIFE SCIENCES

Semester Test

April 2007

Time Allowed: 1.5 hours + 5 min reading time.

TOTAL MARKS: 50

Answer ALL questions.

Closed books, closed notes.

Calculators are permitted.

Reference materials are forbidden.

0701 124.111 Semester Test

of 6

1. The sketches below show three different displacement-time graphs:

(a) (b) (c)

(i) Sketch velocity-time graphs corresponding to (a), (b) and (c). [3 marks]

(ii) For each graph say whether the motion exhibits any acceleration. [3 marks]

(iii) If the displacement-time graph in (b) can be described by

displacement = v0t +1

2at2 , what does that tell you about the

acceleration? [1 mark]

(iv) A balloon is rising vertically at a rate of 3 m s–1

. When it is at a height

of 30 m above the ground a sandbag is released. What is the final

velocity of the bag when it hits the ground? [2 marks]

(v) Sketch a displacement-time graph for the sandbag. [1 mark]

Useful Information:

v = v0 + at

v2= v0

2+ 2ax

x = v0t +1

2at2

x =1

2v + v0( )t

g = 9.8 m s 2

time

disp

lace

men

t


of 6

2. (i) Write down the two conditions necessary for a body to be in equilibrium. [2 marks]

The left-hand diagram above shows schematically a technique for keeping a human

patient’s neck in tension after he has had an accident. The right-hand diagram shows a patient who is kept on a bed inclined at 30° to the horizontal because of fluid retention in his lungs. In order for the traction to be effective it must be large enough to overcome the static frictional force between the patient’s head and the flat head rest. The patient’s head weighs 50 N and the maximum static friction force is 10 N.

(ii) Calculate the forces T and N shown in the right-hand diagram. [3 marks]

The diagram above shows the foot of a 60 kg woman who has put all of her weight on

the ball of her right foot.

(iii) By considering the free-body diagram of the whole woman, show that N = 590 N. [2 marks]

(iv) By taking torques, calculate the tension in the Achilles tendon (FT). [2 marks]

(v) Calculate the compression force in the bone at the ankle (Fc). [1 mark]


of 6

3. Astronauts are launched into space lying on their backs in order that they are facing in the direction of their acceleration. The maximum tolerable acceleration in this orientation is approximately twice the acceleration of gravity (2g).

(i) Calculate the normal force on the back of a 65 kg astronaut during a

launch with an acceleration of 2g. [2 marks]

In order to train for space missions, astronauts are placed in a NASA centrifuge. In this

device they sit upright in a seat at the end of a horizontal 3.4 m long support rod that moves in a horizontal circle as indicated in the diagram above.

(ii) Sketch a diagram to show the velocity of the astronaut and his

acceleration. [1 mark] (iii) What force causes the astronaut’s acceleration? (Hint: “The centripetal

force” is not an adequate answer.) [1 mark]

The centrifuge must simulate the experience of being launched into space.

(iv) Explain why, to ensure the simulation is realistic, the acceleration experienced by the astronaut in the centrifuge must be 3g. [1 mark]

(v) Write down the normal force of the centrifuge’s seat on the

astronaut’s back. [1 mark] (vi) Show that the angular speed of rotation ( ) of the centrifuge is

2.9 radian s–1. [1 mark] (vii) Express this speed in revolution min–1. [2 marks] (viii) Calculate the astronaut’s speed (in m s–1). [1 mark]

Useful Information:

a = 2r

v = r


of 6

4. (a) (i) Explain the difference between heat capacity and specific heat

capacity. [1 mark]

In order to measure the power output of a new laboratory microwave oven, a

technician places 300 gram of water at 22 °C in a 200 gram glass container inside

the oven, closes the door and runs the oven at full power for 50 second. The final

temperature of water and glass mug is 57 °C.

(ii) Calculate the power output of the oven. (Neglect heat losses

from the water.) [4 marks]

(b) The new (American) air conditioner for a small animal practice is rated at

12 000 Btu h–1.

(i) Show that 12 000 Btu h–1 is the same as 3.5 kW. [2 marks]

The heat removed from the surgery by the air conditioner is used to evaporate

water for use in a small tropical animal house.

(ii) Calculate the mass of water vapour generated in one hour by the

heat removed from the surgery. [2 marks]

(iii) Determine the volume of water that this would require. [1 mark]

Useful Information:

Specific heat capacity of glass = 0.670 kJ kg–1 K–1

Specific heat capacity of water = 4.180 kJ kg–1 K–1

Specific latent heat of water = 2.26 MJ kg–1

Density of water = 1 000 kg m–3

1 Btu = 1 055 J

c =Q

m T

Lv =Q

m

=m

V

P =W

t


of 6

5. A researcher wants to examine the elastic properties of the Achilles’ tendon. The

tendon they are working with is 150 mm long, and has a cross-sectional area of

7 10–5

m2. The tendon is hung vertically and a weight of 1960 N is attached to its

end, stretching it by 3.07 mm.

(i) Calculate Young’s modulus for the tendon. [1 mark]

(ii) By considering the forces on the tendon, show that the force constant,

k, is equal to 6.38 105 N m

–1. [1 mark]

(iii) The researcher now starts the mass oscillating, so that it moves in

SHM. Calculate the period of oscillation. [1 mark]

(iv) Write the equation of motion for the mass, given that the amplitude of

oscillation is 1 mm and that it is at maximum amplitude at t = 0. [2 marks]

(v) Sketch a graph of displacement vs. time for the mass. [2 marks]

(vi) At what point in the motion will maximum velocity occur? [1 mark]

(vii) Calculate the displacement at t = 0.15 s. [2 marks]

Useful Information:

Y =tensile stress

tensile strainStrain =

L

L0Stress =

F

A

x(t) = Acos t x(t) = Asin t

T = 2m

k= 2 f

+ + + + + + + +

2007 physics semester test

Documents