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1. How fast is the collision crash of 5,000kg car moving with a velocity of 5.2m/s that hits a stationary 8000kg truck on a frictionless track?
2. A bullet with 2.0 g mass and 300 m/s velocity hits a wooden trolley with 1.5 kg mass which is at rest on a frictionless track. Determine the final velocity of the wooden trolley.
The speed of a car decreases from 40 m/s to 35 m/s at 12 meters. What is the kinetic energy of the car?
Q5. A single bar of material Q of the same cross-sectional area is to be used to allow the same
rate of flow of heat through it as the composite series arrangement when the same temperature
difference exists between its ends. What should be the length of the bar if this rate of flow is
107 W?
A) 0.75 m
B) 0.65 m
C) 1.25 m
D) 1.50 m
Questions 3 – 5 refer to the diagram below, which shows composite bars made from sections of
two metals, P and Q, of conductivities of 400 W m -1 K -1 and 200 W m -1 K -1 respectively. P and Q
are both of cross-sectional area 1.00 X 10 -2 m 2 . The structures are perfectly lagged and a
temperature difference of 40 K is set up across their lengths.
40 K
40 K P
P Q Q
50.0 cm 50.0 cm 50.0 cm
Q3. What is the rate of heat flow under steady state conditions with P and Q in series?
A) 107 W
B) 120 W
C) 480 W
D) 240 W
Note that the effective k for a series composite of two slabs, k series = k 1 k 2 / (k 1 + k 2 )
Q4. What is the rate of heat flow under steady state conditions with P and Q in parallel?
A) 120 W
B) 480 W
C) 240 W
D) 107 W
Note that the effective k for a parallel composite of two slabs, k parallel = k 1 + k 2
An aluminium bar of length 45.0 cm and a steel bar of length 60.0 cm and same cross-
section area are joined thermally end-to-end (see diagram below). The aluminium end is kept at
350 0 C and the steel end at 80.0 0 C. [k aluminium = 200 W/m K, k steel = 40 W/mK]
Aluminium Steel
350 0 C 80.0 0 C
T jxn = ?
Q6 cont’d.
a) Find the temperature where the 2 metals are joined. (Use example given in class)
b) Draw a graph of temperature versus length, x, for the compound bar.
A copper rod and a silver rod of the same length and cross-sectional area are attached
end-to-end (see figure below). The copper end is placed in a furnace maintained at a constant
temperature of 225 0 C. The silver rod is place in an ice bath held at constant temperature of 0.0
0 C. Calculate the temperature at the point where the two rods are joined. (Use example given in
class.) [k copper = 380 W m -1 K -1 and k silver = 420 W m -1 K -1 ]
Copper Silver
225 0 C 0.0 0 C
T jxn = ?
This question refers to a perfectly lagged bar comprised of materials X, Y and Z of
conductivities k x , k y , and k z respectively. The graph shown indicates the variation of temperature
θ with distance D from the hotter end of the bar when a temperature difference is set up across
the length. Steady state conditions prevail and each material is of length 20 cm.
Lagged bar
110 0 C X Y Z 25 0 C
θ / 0 C D/cm
110
25
20 40 60 D/cm
X Y Z
Which of the following is true of the conductivities of X, Y and Z?
A) k x > k y > k z
B) k x > k z > k y
C) k y > k z > k x
D) k z > k x > k y
A box is sitting on a ramp
angled at 20°. If the box weighs
50 N, what is the normal force
on the box?
A lady is weighing some bananas in a grocery store when the floor
collapses. If the banana's mass is 2 kg and the floor is accelerating
at -2.25 m/s2, what is the apparent weight (normal force) of the
bananas?
A 60 – g rifle bullet leaves the muzzle with a velocity of 600 m/s. The 3.0 kg rifle is held firmly by a 60.0 – kg man. With what velocity will the man and rifle recoil?
