3.2 Problems
111
3.19 In prob. (3.18), show that the minimum frequency for which the block will not
move with respect to the funnel will be
f min =
1
2π
g(sin θ − μ cos θ)
r (cos θ + μ sin θ)
3.20 A large mass M and a small mass m hang at the two ends of a string that
passes through a smooth tube as in Fig. 3.6. The mass m moves around in a
circular path which lies in a horizontal plane. The length of the string from the
mass m to the top of the tube is L, and θ is the angle this length makes with
the vertical. What should be the frequency of rotation of the mass m so that
the mass M remains stationary?
[Indian Institute of Technology 1978]
Fig. 3.6
3.21 An object is being weighed on a spring balance going around a curve of radius
100 m at a speed of 7 m/s. The object has a weight of 50 kg wt. What reading
is registered on the spring balance?
3.22 A railway carriage has its centre of gravity at a height of 1 m above the rails,
which are 1.5 m apart. Find the maximum safe speed at which it could travel
round the unbanked curve of radius 100 m.
3.23 A curve on a highway has a radius of curvature r . The curved road is banked
at θ with the horizontal. If the coefficient of static friction is μ,
(a) Obtain an expression for the maximum speed v with which a car can go
over the curve without skidding.
(b) Find v if r = 100 m, θ = 30 ◦ , g = 9.8 m/s 2 , μ = 0.25
3.24 Determine the linear velocity of rotation of points on the earth’s surface at
latitude of 60 ◦ .
3.25 With what speed an aeroplane on the equator must fly towards west so that the
passenger in the plane may see the sun motionless?
111
3.19 In prob. (3.18), show that the minimum frequency for which the block will not
move with respect to the funnel will be
f min =
1
2π
g(sin θ − μ cos θ)
r (cos θ + μ sin θ)
3.20 A large mass M and a small mass m hang at the two ends of a string that
passes through a smooth tube as in Fig. 3.6. The mass m moves around in a
circular path which lies in a horizontal plane. The length of the string from the
mass m to the top of the tube is L, and θ is the angle this length makes with
the vertical. What should be the frequency of rotation of the mass m so that
the mass M remains stationary?
[Indian Institute of Technology 1978]
Fig. 3.6
3.21 An object is being weighed on a spring balance going around a curve of radius
100 m at a speed of 7 m/s. The object has a weight of 50 kg wt. What reading
is registered on the spring balance?
3.22 A railway carriage has its centre of gravity at a height of 1 m above the rails,
which are 1.5 m apart. Find the maximum safe speed at which it could travel
round the unbanked curve of radius 100 m.
3.23 A curve on a highway has a radius of curvature r . The curved road is banked
at θ with the horizontal. If the coefficient of static friction is μ,
(a) Obtain an expression for the maximum speed v with which a car can go
over the curve without skidding.
(b) Find v if r = 100 m, θ = 30 ◦ , g = 9.8 m/s 2 , μ = 0.25
3.24 Determine the linear velocity of rotation of points on the earth’s surface at
latitude of 60 ◦ .
3.25 With what speed an aeroplane on the equator must fly towards west so that the
passenger in the plane may see the sun motionless?