ASSIGNMENT-2: GPS115B [38 Marks]
[5 marks] Question1
At the local swimming hole, a favorite trick is to run horizontally off a cliff that is 8.3 m above
the water, tuck into a ``ball,’’ and rotate on the way down to the water. The average angular
speed of rotation is 1.6 rev/s. Ignoring air resistance,
[5]
determine the number of revolutions while on the way down.
[8 marks] Question2
2.1 The drill bit of a variable-speed electric drill has a constant angular acceleration of
2.50 rad/s2. The initial angular speed of the bit is 5.00 rad/s. After 4.00 s, calculate
the
2.1.1Angular displacement that the bit has turned through.
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2.1.2 Bit’s angular speed.
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2.2 A centrifuge in a medical laboratory rotates at an angular speed of 3 600 rev/min.
When switched off, it rotates through 50.0 revolutions before coming to rest.
Calculate the constant angular acceleration of the centrifuge.
[3]
[7 marks] Question3
Consider the steady laminar flow of a fluid through an enclosed tube or pipe as
depicted in Figure 1. The speed of the fluid varies as the diameter of the tube changes.
The mass flow rate is defined as the mass 𝛥m of the fluid that passes a given point per
unit time 𝛥t.
𝛥x1
𝛥x2
Figure 1
3.1. Derive equation of continuity. (Hint: ρ1 = ρ2 = ρ)
[4]
3.2. A liquid (ρ = 1.65 g/cm3) flows through two horizontal sections of tubing joined
end to end. In the first section, the cross-sectional area is 10.0 cm2, the flow speed is
275 cm/s, and the pressure is 1.20 x 105 Pa. In the second section, the crosssectional area is 2.50 cm2. Determine the flow of speed in a smaller section.
[3]
[5 marks] Question4
4.3 A student drops two metallic objects into a 120 g steel container holding 150 g of
water at 25°C. One object is a 200 g cube of copper that is initially at 85°C, and the
other is chunk of aluminium that is initially at 5°C. To the surprise of the student, the
final equilibrium temperature of 25°C is reached. What is the mass of the aluminium
chunk?
[5]
Additional questions
[13 marks] Question 5
5.1. Define work energy theorem.
[2]
5.2. A 750-kg automobile is moving at 20.0 m/s at a height of 5.0 m above the bottom
of a hill when it runs out of gasoline. The car coasts down the hill and then
continues coasting up the other side until it comes to rest, as shown in Figure 2.
Ignoring frictional forces and air resistance, what is the value of h, the highest
position the car reaches above the bottom of the hill? [5]
Figure 2
5.3. Two forces ⃗⃗⃗
𝐹1 = (1.50𝑖 − 0.8 𝑗 + 0.70𝑘)𝑁 and ⃗⃗⃗
𝐹2 = (−0.70 𝑖 + 1.20 𝑗)𝑁 are
applied on a moving object of mass 0.20 kg. The displacement vector produced
by the two forces is 𝑑 = (8.0𝑖 + 6.0𝑗 + 5.0𝑘)𝑚.
5.3.1. Calculate the work done by the two forces.
5.3.2. Calculate the angle between the resultant force F and displacement d.
[3]
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