**Third Examination
**

Physics 103

25 November 1980
#1. Three masses are positioned as shown:

**2 kg at (2, 0) meters
**

1 kg at (-1, 2) meters

3 kg at (-1,-1) meters

The coordinates of the ** center of mass** of the system (**in meters**) are: :

**Answer:**

#2. A ** 70 kg ** man on a ** 20 kg** boat walks ** 3 meters** forward, as measured on the
boat. How far ** backward** does the boat move, ** relative to a nearby
pier**.

**Note**: Neglect drag effects of the water.

**Answer:**

#3. Two particles, each of mass ** m**, are placed initially at rest
along the **x-axis**, one at ** x = +L **and the other at ** x= -L**

A constant force **F**_{0 }j
acts on the mass initially located at ** x = +L** for a time **T**. There is no
force acting on the mass at ** x = -L**. At the end of time ** T** the
** center of mass ** is located at

**Answer:**

#4. The **thrust **[thrust is a force] required to accelerate a **20,000
kg** rocket **upward **at an acceleration of **10 m/sec**^{2}_{
}on the moon, where **g = 1.6 m/sec**^{2}, is most nearly equal to

**Answer:**

#5. A modern aircraft cannon can fire **100 two-kilogram shells per
second**. If the muzzle velocity is ** 500 meters/second,** the average
"**recoil force**" exerted on the gun mounting is approximately

**Answer:**

#6. A particle of mass **2 kilograms** is subject to the**
time-varying force** given in the graph. If the ** velocity** of the particle at
time **t = 0** is** zero**, the **velocity after three second**s is equal to

**Answer:**

#7. An object, initially at rest, explodes into **three **pieces. Two
pieces of **equal mass** travel along the** x-axis** and **y-axis**,
respectively, with the same speed of **10 m/sec**. The speed of the **third
piece**, having a mass **twice** that of each other pieces, is about

**Answer:**

#8. A block of mass **m**_{A} traveling on a frictionless horizontal
table with a speed **v**_{A }collides elastically with a block of
different mass **m**_{B}. the block of mass **m**_{B}
is initially at rest. **Note**: this is a **one-dimensional**
collision The **speed** of **m**_{B }after the collision is
equal to

**Answer:**

#9. Two objects of equal mass ** m** are heading toward one another with equal speeds
**
v.** A massless spring of spring constant ** k** is attached to one of the
objects as shown. In the ** one dimensional elastic collision ** of the objects,
the ** maximum distance** by which the spring is ** compressed ** is:

**Answer:**

#10. A **2 kg** block hangs at rest from a wire attached to the
ceiling. It is hit by a **0.05 kg** bullet traveling horizontally at **200
m/sec**. If the collision is perfectly inelastic, the **vertical
distance above** the original position to which the block and bullet rise is
about:

**Answer:**

#11. An auto (**weight = 3200 lb**) traveling **East** at **45 ft/sec**
collides with a truck (**weight = 9600 lb**) traveling **North** at **30
ft/sec**. If the collision is perfectly inelastic, the **loss in
kinetic energy** of the system (**in ft-lb**) is approximately

**Answer:**

#12. As shown in the sketch, a large particle (**mass 2m**) moves along the **+x-direction**
with a small particle (**mass m**) initially at rest. After the collision, the
small particle is found moving with a velocity ** Ö3
v**_{0} at an angle of ** 30**^{o} with respect to the ** x-direction** (see sketch).
The ** velocity** (**magnitude; angle below x-axis)** of the ** large** particle after the collision equals

**Answer**

#13. A stereo turntable accelerates **uniformly from rest to 33 rev/min in 1.5
seconds**. The **number of revolutions** the turntable makes in the **1.5
seconds is** about

**Answer**

14. The **angular acceleration** of a bicycle wheel is constant at **-0.10
rad/sec**^{2} (**clockwise**). If its initial angular speed
is **4.0 rad/sec**^{2} (**counter-clockwise**), the **net
number of (counter-clockwise) revolutions** it will have made at the end of **30
seconds** is most nearly equal to

**Answer:**

#15. An automobile is traveling at **22 ft/sec**(**15 mph**).
If the **radius** of a tire on this auto is **1 ft**, what is the **angular
velocity** of the tire **in rad/sec**? (Assume that the tire rolls
without slipping.)

**Answer:**