**Final Examination
**

Physics 103

15 December 1980
#1. The **angle** between the vectors **A
= 6 i - 3 j
+ 2 k** and **B
= 3 i + 4
j **is most nearly equal to

**Answer:**

#2. The **displacement vs time** graph of moving automobile is
given as shown. The **average speed** of the automobile between **0
sec** and **3 sec** is approximately

**Answer:**

#3. An el train a**ccelerates from rest at **one station at 1 m/sec^{2
}for half the distance to the next station; then it **decelerates at this
same rate** for the final half. If the stations are **2 km **apart, **how
long **does it take the train to travel between stations?

**Answer:**

#4. A gun shoots a dart at an angle of **60**^{o} above the
horizontal. The dart lands a horizontal distance **10 meters **away
from the gun muzzle. What is the **speed** of the dart as it leaves the
gun?
**Answer:**

#5. The earth rotates once about its axis in about **24 hours**.
The magnitude of the **centripetal acceleration** of an object on the
equator is most nearly equal to (__Note__: Radius of the earth
is **6.37 ´ 10**^{6} m.)

**Answer:**

#6. A block of mass M is at rest on a horizontal, frictionless
surface. It is attached to a massless cord which is passed over a
frictionless, massless pulley to another mass,** m,** which is hanging
freely. See sketch. The system is then released from rest. The
**tension in the cord** is

**Answer:**

#7. A **50 kg** box rests on a horizontal floor with coefficient of friction **µ
= 0.4** (Assume** µ**_{s} = µ_{k}.) The **horizontal
force** (**in Nt**) required to accelerate the box at **0.5 m/sec**^{2}
is about

**Answer:**

#8. A block of mass ** m** ** is moving** on a rough horizontal surface in the direction
of the positive x-axis, while somebody is pulling on it with a force of
magnitude **F**, directed at an angle
**q** with respect to the horizontal.
The coefficient of sliding friction is **µ**. The **total force**
of the **table** on the **block** is

**Answer:**

#9. A box of mass **m = 1.5 slugs** compresses a spring (**k = 3000 lb/ft**)
by **0.3 ft**. After it is released, the box slides for **8 ft** on
a rough level surface (**µ**_{K} = 0.3). Its speed (**in
ft/sec**) after sliding **8 ft** is about

**Answer:**

#10. (__Note__: See figure for previous problem.) Assuming
the velocity of the mass is **V**_{0} as it leaves the surface, if
the height **h** is known, then **x** (the horizontal distance the mass
travels before hitting the ground) is given by:
**Answer:**

#11. A toy gun is powered by a spring (**spring constant k**). It is
loaded with a dart (**mass m**) and the spring is compressed by an amount**
x**. The dart is then fired **vertically upward** from the gun.
Assuming that only conservative forces are present, the **height** to which
the dart rises above its initial position is equal to

**Answer:**

#12. The loaded cab of an elevator has a mass of **3000 kg** and moves **200
meters** up the shaft in **20 sec**. The **average power** (**in
Watts**) is most nearly equal to

**Answer:**

#13. A small particle of **mass m** is attached to the **perimeter** of a **uniform
disc** of **radius R** and **mass M**. The **center of mass**
of the resulting combination is a **distance from the center** of the disc
equal to
**Answer:**

#14. A **0.5 kg** baseball travels toward a batter at **40 m/sec**.
The batter hits the ball, imparting an **average force** of **900 Nt** for
**50 milliseconds** to the ball. If the ball reverses direction, its **final
speed** (**in m/sec**) is most nearly equal to

**Answer:**

#15. A stream of small balls strikes a wall normally and rebounds
elastically. If the balls have a **mass** of **0.25 ´
10**^{-3 }kg each, a speed of **100 m/sec**, and strike the
wall at a rate of **100 per second**, the magnitude of the **average force**
imparted to the wall by the balls **in one second** is equal to

**Answer:**

#16. In a football game, a player weighting **256 lb** runs toward the ball
carrier at 20 ft/sec. The ball carrier weight **192 lbs** and is
running toward the player with a speed of **30 ft/sec**. If the collide
in a tackle which is **perfectly inelastic**, their **final speed** is
about

**Answer:**

#17. ** **An object of mass **1.0 kg**, traveling North with a speed
of **400 m/sec**, explodes into **two pieces of equal mass**. After
the explosion, one piece travels due West with a speed of **600 m/sec**.
The other piece will have a ** momentum** of magnitude (**in kg m/sec**)

**Answer:**

#18. A railroad car (**m = 30,000 kg**) with an initial velocity of **5
m/sec **collides **elastically** with another car of **equal mass**,
initially at rest. The **velocity** of the **second car after the
collision** is

**Answer:**

#19. A straight uniform rod is constrained to rotate about a **vertical axis**
through its midpoint. Its **moment of inertia** about this axis is **0.5
kg m**^{2}. It is observed to make** 45 revolutions** before
coming to rest in **30 seconds**, because of a **constant frictional torque**
at the axis. The value of the **constant angular acceleration** (**in
revolutions/sec**^{2}) is most nearly equal too

**Answer:**

#20. Referring to** Problem #19**, the **frictional torque (in
Newton-meters)** is most nearly equal to

**Answer:**

#21. A grinding wheel of radius **5 cm **is accelerated at a constant
angular acceleration of **15 rad/sec**^{2}. the wheel starts
from rest at time **t = 0 sec**. At time **t = 2 sec**, a particle
flies off the edge of the wheel. The **linear velocity** with which the
particle flies off (**in meters/sec**) is approximately

**Answer:**

#22. Two particles, each of mass **1 kg**, are moving in the **x-y plane**
as shown. The first, located at (**x = 1 meter, y = 1 meter**), has a
velocity of **1 meter/sec** to the left. The second, located at (**-1
m, -1 m**), has a velocity of **1 meter/sec** to the right. The **angular
momentum **of the two particles about the origin (**in SI units**) is

**Answer:**

#23. Three equal masses, **M**, lie in a plane at the corners of an
equilateral triangle of side **L**. the **rotational inertia**
(moment of inertia) of the three-mass system about an axis perpendicular
to the plane of the triangle and passing through the center of mass is
**Answer:**

#24. A hollow ball (**I**_{cm} = 2M R^{2} /3), initially
traveling at a velocity **v**_{cm} (without sliding), rolls up
an incline with angle **q** as measured from
the horizontal. Assuming **R** is small compared with **H**, the
height **H** that the ball travels before coming to rest is given by
**Answer:**

#25. On the evening of December 24, a man of **mass m** wishes to descend a
chimney of **height H**. In order to do so, he wraps a rope of
negligible mass about the rim of a **wheel of mass M and radius R**,
With the wheel initially at rest, he grasps the rope and steps into the
chimney. Assume that the wheel is a uniform disk. The **speed of
the man** as he reaches the bottom of the chimney is
**Answer:**