It is well known that a
raindrop falls under the influence of the
downward gravitational force and the
opposing resistive force. The latter is knownto be proportional to the speed of the drop
but is otherwise undetermined. Consider
a drop of mass 1.00 g falling from a height
1.00 km. It hits the ground with a speed of
50.0 m s-1. (a) What is the work done by the
gravitational force ? What is the work done
by the unknown resistive force?
Find the angle between force
F = (3 +4 -5 ) ˆ ˆ ˆ i j k unit and displacement
d = (5 + 4 +3 ) ˆ ˆ ˆ i j k unit. Also find the
projection of F on d.
A family uses 8 kW of power. (a) Direct solar energy is incident on the horizontal
surface at an average rate of 200 W per square meter. If 20% of this energy can be
converted to useful electrical energy, how large an area is needed to supply 8 kW?
(b) Compare this area to that of the roof of a typical house.
A person trying to lose weight (dieter) lifts a 10 kg mass, one thousand times, to a
height of 0.5 m each time. Assume that the potential energy lost each time she
lowers the mass is dissipated. (a) How much work does she do against the gravitational
force ? (b) Fat supplies 3.8 × 107J of energy per kilogram which is converted to
mechanical energy with a 20% efficiency rate. How much fat will the dieter use up?
The blades of a windmill sweep out a circle of area A. (a) If the wind flows at a
velocity v perpendicular to the circle, what is the mass of the air passing through it
in time t ? (b) What is the kinetic energy of the air ? (c) Assume that the windmill
converts 25% of the wind’s energy into electrical energy, and that A = 30 m2
, v = 36
km/h and the density of air is 1.2 kg m–3. What is the electrical power produced ?
A body of mass 0.5 kg travels in a straight line with velocity v =a x
3/2 where a = 5 m–1/2 s–1
.
What is the work done by the net force during its displacement from x = 0 to
x = 2 m ?
A trolley of mass 300 kg carrying a sandbag of 25 kg
is moving uniformly with a speed of 27 km/h on a
frictionless track. After a while, sand starts leaking
out of a hole on the floor of the trolley at the rate of
0.05 kg s–1. What is the speed of the trolley after the entire sand bag is empty ?
The bob of a pendulum is released from a horizontal
position. If the length of the pendulum is 1.5 m,
what is the speed with which the bob arrives at the
lowermost point, given that it dissipated 5% of its
initial energy against air resistance ?
The bob A of a pendulum released from 30o
to the
vertical hits another bob B of the same mass at rest
on a table as shown in Fig. 5.15. How high does
the bob A rise after the collision ? Neglect the size of
the bobs and assume the collision to be elastic.
Two identical ball bearings in contact with each other and resting on a frictionless
table are hit head-on by another ball bearing of the same mass moving initially with a
speed V. If the collision is elastic, which of the following (Fig. 5.14) is a possible result
after collision ?
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