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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