HOMEWORK SET 1
2.22
A car of mass 1775 kg travels with a velocity of 100 km/h. Find the kinetic
energy. How high should it be lifted in the standard gravitational field to have a
potential energy that equals the kinetic energy?
Solution:
Standard kinetic energy of the mass is
KIN = ½ m
V
2
= ½
×
1775 kg
×
⎝
⎜
⎛
⎠
⎟
⎞
100
×
1000
3600
2
m
2
/s
2
= ½
×
1775
×
27.778 Nm = 684 800 J
=
684.8 kJ
Standard potential energy is
POT = mgh
h = ½ m
V
2
/ mg
=
684 800 Nm
1775 kg
×
9.807 m/s
2
=
39.3 m
2.29
A hydraulic lift has a maximum fluid pressure of 500 kPa. What should the
piston-cylinder diameter be so it can lift a mass of 850 kg?
Solution:
With the piston at rest the static force balance is
F
↑
= P A = F
↓
= mg
A =
π
r
2
=
π
D
2
/4
PA = P
π
D
2
/4 = mg
⇒
D
2
=
4mg
P
π
D = 2
mg
P
π
= 2
850 kg
×
9.807 m/s
2
500 kPa
×
π
×
1000 (Pa/kPa)
=
0.146 m

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