of
N measurements x1,…, xN, one need the
sum
.
Prove that this sum can be rewritten as
QUESTIONS (Don’t forget to show all yourwork!)
Click in the links below to go directly to a particular week.
1) To
compute the standard deviation
of
N measurements x1,…, xN, one need the
sum.
Prove that this sum can be rewritten as
2) A student measures a quantity x five times, with the results 5, 7, 9, 7, 8. Calculate the mean and the standard deviation. (Do the calculation yourself; don’t just press the appropriate buttons on you calculator.)
1) If an object is moving at uniform speed in a straight line, its instantaneous velocity halfway through any time interval is
Greater than its average velocity.
Less than its average velocity.
The same as its average velocity.
Half of its average velocity.
Twice its average velocity.
2) On a graph that shows position on the vertical axis and time on the horizontal axis, a straight line with a positive slope represents.
A constant positive acceleration.
A constant negative acceleration.
Zero velocity.
A constant positive velocity.
A constant negative velocity.
3) On a graph that shows velocity on the vertical axis and time on the horizontal axis, the area under the curve represents.
1) A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. What is the angle of projection?
2) A soccer player kicks a rock horizontally off a cliff 40.0 m high into a pool of water. If the player hears the sound of the splash 3.00 s later, what was the initial speed given to the rock? Assume the speed of sound in air to be 343 m/s.
3) A projectile is shot at an angle of 45 degrees to the horizontal near the surface of the earth but in the absence of air resistance. When it reaches the highest point of its trajectory, its speed is 150 m/s. In a second trial with the same projectile, the initial speed is the same but the angle is now 37 degrees with the horizontal. At its highest point in this trajectory, the speed of the projectile would be:
a) 150 m/s (sin 45 / sin 36)
b) 150 m/s (cos 37 /cos 45)
c) 150 m/s (sin 37 / sin 45)
d) 150 m/s (37 / 45)
Do the following problems from your lecture textbook.
1)
Two forces F1 and F2 are acting on a box as the
box slides rightward across a frictionless floor. Force F1 is
horizontal, with magnitude 2.0 N; force F2 is angled
upward by 60o to the floor and has a magnitude 4.0 N. The
speed v of the box at a certain instant is 3.0 m/s.
a) What
is the power due to each force acting on the box at that instant,
b) What is the net power?
c) Is the net power changing at
that instant?
2)
A force of 5.0 N acts on a 15 Kg body initially at rest. Compute:
a) The work done by the force in the first, second, and third
seconds
b) The instantaneous power due to the force at the
end of the third second.
1) Does the force of gravity affect the horizontal component of the projectile’s velocity? Why?
2) If the projectile should be fired with a higher initial (or muzzle) velocity, would the range be greater? Would the time of fall be different? Explain.
3)
If the spring gun were carried to a place where g = 900 cm/sec2,
and fired with the same initial velocity, would the range be
different? Explain.
1)
With a given radius, what effects does
indicate
that an increased velocity would have on the centripetal force
required to maintain uniform motion in the same circle?
2)
Imagine you add mass to the bob in today’s experiment, while
keeping the radius constant. How are the frequency and force affected
as a result? Explain the reasons for the resulting effect on each of
these quantities.
1) In making your theoretical calculation, do you think a correction should be made for the hole in the center of the disk? Why?
2)
Are the moments of inertia of the ring and the disk directly
proportional to their respective masses? Explain why.