Physics homework #07

1. Solve the problems presented on Fig. 1. Values of m, α, β, and θ are known, and m is a point mass.

Fig. 1

Fig. 2

2. If you have to lift a 10-kg, 2-m board, common sense prompts you to pick up the long board at its

centre because it balances more easily. If you were able to lift the board by it’s end, with your fingers
extending 15 cm under the board (Fig. 2), how much force would you have to exert?

3. The horizontal beam in Fig. 3 weighs 150 N, and

its centre of gravity is at its centre. Find (a) the
tension in the cable and (b) the horizontal and
vertical components of the force exerted on the
beam at the wall.

Fig. 3

4. At what altitude above a planet having radius R is the acceleration due to gravity one half of that

at its surface?

5. A particle is released at rest at an altitude above the earth’s surface equal to the radius R

E

of the

earth. Find its speed v as it strikes the earth. Neglect the air resistance. The mass of the earth is
M

E

.

6. In Jules Verne’s 1865 story “From the earth to the moon”, three men were sent to the moon in a

shell fired from a giant cannon. (a) Find the muzzle speed needed to shoot the shell straight up
to a height above the earth equal to the earth’s radius. (b) Find the escape speed – that is, the
muzzle speed that would allow the shell to escape from the earth completely. (R

E

= 6380 km,

M

E

= 5.97 × 10

24

kg)

7. Show that for altitudes y that are small compared to the radius of the earth R

E

, the gravitational

potential energy can be approximated by the function U (y) = mgy.
(Hint: Use Taylor series for f (

y

R

) = (1 +

y

R

)

−1

.)

8. 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)

9. 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.

10. 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.

11. 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?

Maciej Wo loszyn

WFiIS AGH

http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/