Physics tutorial #10

1. At the local airport, a person carries a 21 kg suitcase in one hand. Assuming the humerus (the upper

arm bone) supports the entire weight of the suitcase, determine the amount by which it stretches.
(The humerus may be assumed to be 33 cm in length and to have an effective cross-sectional area
of 5.2 × 10

−4

m

2

. The Young’s modulus is 1.6 × 10

10

N/m

2

.)

2. In constructing a large mobile, an artist hangs an aluminum sphere of mass 6.0 kg from a vertical

steel wire 0.5 m long and 2.5 × 10

−3

cm

2

in cross-sectional area. On the bottom of the sphere he

attaches a similar steel wire, from which he hangs a brass cube of mass 10.0 kg. For each wire,
compute (a) the tensile strain and (b) the elongation. (For steel Y = 2 × 10

11

Pa)

3. Outside a house 1.0 km from ground zero of a 100-kiloton nuclear bomb explosion, the pressure will

rapidly rise to as high as 2.8 atm while the pressure inside the house remains 1.0 atm. If the front
of the house measures 3.33 m high by 15.0 m wide, what is the resulting net force exerted by the air
on the front of the house?

4. A steel cable with cross-sectional area 3.0 cm

2

has an elastic limit of 2.4×10

8

Pa. Find the maximum

upward acceleration that can be given a 1200-kg elevator supported by the cable if the stress is not
to exceed one-third of the elastic limit.

5. A brass wire is to withstand a tensile force of 350 N without breaking. What minimum diameter

must the wire have? The breaking stress of brass is 4.7 × 10

8

Pa.

6. A 1.05-m-long rod of negligible weight is supported at its ends by wires A and B of equal length.

The cross-sectional area of A is 2.0 mm

2

and that of B is 4.0 mm

2

. Young’s modulus for wire A

is 1.8 × 10

11

Pa; that for B is 1.2 × 10

11

Pa. At what point along the rod should a weight w be

suspended to produce (a) equal stresses in A and B, and (b) equal strains in A and B?

7. A 2.2-kg mass oscillates on a spring of force constant 250.0 N/m with a period of 0.615 s. (a) Is this

system damped or not? How do you know? If it is damped, find the damping constant b. (b) Is the
system undamped, underdamped, critically damped, or overdamped? How do you know?

8. An unhappy 0.3-kg rodent,moving on the end of a spring with force constant k = 2.5 N/m, is acted on

by a damping force F

x

= −bv

x

. (a) If the constant b has the value 0.9 kg/s, what is the frequency of

oscillation of the rodent? (b) For what value of the constant b will the motion be critically damped?

9. A sinusoidally varying driving force F (t) = F

max

cos ω

d

t is applied to a damped harmonic oscillator

of force constant k, mass m and the damping constant b. (a) What are the units of the damping
constant b? (b) Show that the quantity

√

km has the same units as b. (c) In terms of F

max

and k,

what is the amplitude for ω

d

=

q

k/m when (i) b = 0.2

√

km and (ii) b = 0.4

√

km?

10. A mass m is attached to one end of a massless spring with a force constant k and an unstretched

length l

0

. The other end of the spring is free to turn about a nail driven into a frictionless, horizontal

surface (see figure). The mass is made to revolve in a circle with an angular frequency of revolution
ω

0

. (a) Calculate the length l of the spring as a function of ω

0

. (b) What happens to the result in

part (a) when ω

0

approaches the natural frequency ω =

q

k/m of the mass-spring system?

Nivas Babu Selvaraj, Maciej Wo loszyn
http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/