PHYS 150 TEST #4 ; 12/07/07 ; Dr. Holmes ;
NAME:
DO ALL SEVEN PROBLEMS. THE WORTH OF EACH PART
OF EACH PROBLEM IS MARKED NEXT TO THE SLOT FOR THE ANSWER. SHOW YOUR WORK FOR
PARTIAL CREDIT. ALL ANSWERS SHOULD BE IN MKS UNITS UNLESS OTHERWISE INDICATED.
1) A car accelerates from 0 m/s to 20 m/s at a constant rate in 8 seconds on wheels of radius 42 cm. Assume that the tires do not slip.
a) What is the acceleration of the car during the 8 seconds?
2.5 m/s2.
b) What is the angular acceleration of the wheels during the 8 seconds?
5.95 rad/sec2.
c) What is the final angular speed (in rad/sec) of the wheels?
47.6 rad/sec.
d) How many revolutions did the wheels make during the 8 seconds?
30.32 revs.
e) What was the radial acceleration of a point on the outside edge of the wheel at the half way mark (4 second mark) compared to that at the full 8 second mark: [the same, less than half, half, more than half] ?
Less than half.
f) What was the tangential acceleration of a point on the outside edge of the wheel at the half way mark (4 second mark) compared to that at the full 8 second mark: [the same, less than half, half, more than half] ?
Same.
2) ) Consider a board of weight 180 Nt and length
2.4 meters with a box of weight 800 Nt located 40 cm from the left end. Two people lift the board by applying an upward
force at each end.
a) How much force must the person on the right (Fright) exert?
223.33 Nt.
b) Will the person on the left have to exert more, the same, or less force than the person on the right?
More.
c) If the weight were moved further to the right (e.g., to 60 cm instead of 40 cm from the left end), would your answer to part a above (force of the right hand) be more, the same, or less?
More.
d) If the board were 2.0 meters long (instead of 2.4 meters) but still had the same 180 Nt weight and the box was still 40 cm from the left end as in part a, would the answer to part a be more, the same, or less?
More.
3) Consider a regular yoyo of inside radius 0.2
cm, outside radius 8 cm, mass 600 gm, and moment of
inertia 9.2 x 10-4 kg-m² . The string is wound around the inside of the
yoyo so that it comes out on the bottom side parallel to the horizontal. The string is pulled to the right with a
force (T) of 0.14 Nt.
a) On the diagram draw arrows and label the arrows to indicate all the forces on the yoyo. Be sure to indicate on the diagram WHERE the forces act as well as the DIRECTION in which they act.
b) What force(s) cause a forward (clockwise) torque on the yoyo?
Ff (friction).
c) What force(s) cause a backward (counterclockwise) torque on the yoyo?
T (tension in the string).
d) What force(s) push the yoyo forward (to the right)?
T (tension in the string).
e) What force(s) push the yoyo backward (to the left)?
Ff (friction).
f) Which way does the yoyo actually end up going? (forward [right], or backward [left])?
Forward (right).
g) Set up the equations from Newton's Second Law (both for forces and torques):
4) Two cylinders are to be rolled down an
incline which has a constant slope that makes an angle, q, with the
horizontal. Assume q is greater
than zero degrees but less than 90 degrees.
Also assume there is enough friction to cause the objects to roll
without slipping. Also assume that the
objects will be going slow enough so that we can neglect air resistance.
a) If the cylinders have the same mass (m1
= m2) but r1 > r2, which one will win a
race down the ramp? (#1, #2, it will be a tie, can’t tell because it depends on
q):
A tie.
b) If the cylinders have the same radius (r1 = r2) but m1 > m2, which one will win a race down the ramp? (#1, #2, it will be a tie, can’t tell because it depends on q):
A tie.
c) If cylinder #2 is replaced by a ring (hollow cylinder) with the same mass and radius as cylinder #1, which object will win the race down the ramp? (cylinder, ring, it will be a tie, can’t tell because it depends on q).
Cylinder wins.
d) If cylinder #2 is replaced by a solid sphere (ball) with the same mass and radius as cylinder #1, which object will win the race down the ramp? (cylinder, sphere (ball), it will be a tie, can’t tell because it depends on q).
Sphere (ball) wins.
e) If h =52 cm, m1 = 90 grams, r1 =3 cm, and q=30°, what will be the speed of cylinder #1 as it reaches the floor if it is released from rest at the top of the ramp?
2.34 m/s.
f) Since there is friction (to make the objects roll), is there any energy lost to friction?
No.
g) Explain your answer to part f above:
5) A spring of spring constant, k, is attached to a mass, m. It is stretched some distance, A, beyond its equilibrium point and then released. Assume that there is no friction and no other forces besides that due to the spring.
a) Design a system that will give a period of oscillation of 0.65 seconds; i.e., specify the following:
k =
m =
A = .
b) If you desired to have a period of oscillation that was twice as long (1.30 seconds), would you choose a spring that has a spring constant that is: [the same, twice as big, four times as big, half as big, one fourth as big, can’t do it since time does not depend on mass] as you used in part a above if you kept the mass and amplitude constant?
1/4 times as big.
c) If instead of changing the spring, you wished to change the mass to get a period of oscillation that was twice as long (1.30 seconds), would you choose a mass that was: [the same, twice as big, four times as big, half as big, one fourth as big, can’t do it since time does not depend on amplitude] as you used in part a above if you kept the same amplitude and spring constant?
4 times as big.
6. a) What is the power output of an electric motor that supplies a torque of 0.25 Nt*m to a wheel that rotates at 4,000 rpm (revolutions per minute)?
104.7 Watts.
b) If the same torque of 0.25 Nt*m is applied but the motor rotates ten times slower at 400 rpm, does the power output of the motor: [decrease by a factor of 1/100, decrease by 1/10, stay the same, increase by a factor of 10, or increase by a factor of 100] ?
Decrease by factor of 1/10.
7) Three identical yoyos have the shape of a cylinder, have a mass, M, large radius, R, and small radius, r, where r << R. You can assume the moment of inertia of each yoyo is simply that of a cylinder (of mass M and radius R). The string of the first yoyo is would around the inside (small) radius and is tied to a fixed rod. The second yoyo's string is NOT attached to anything. The third yoyo has its string would around its large radius, R, so it acts as an inverse yoyo, and its string is also tied to a fixed rod. All three objects are released from rest and allowed to drop down a distance, h. Neglect air resistance.
a) Which of the three objects will reach the ground first (regular, unattached, inverse, all three tie, or two of the three tie)?
Unattached.
b) Which of the three objects will reach the ground last (regular, unattached, inverse, all three tie, or two of the three tie)?
Regular yoyo.
c) Do the strings, which are attached to fixed rods, do any work on the regular and inverse yoyos?
No.
d) Since all three yoyos start out with the same potential energy and the same zero kinetic energy, if the answer to part b is NOT a three way tie, then where did the initial energy go to cause the one (or two) yoyos to be last (to be slower and have less final regular kinetic energy than the winner)? [If all three did tie, then write NA (not applicable) for this answer]?
Into rotational KE.
Assume M = 90 grams, Routside = 3 cm; Rinside = 2 mm; I = 4 x 10-5 kg*m2; and h = 80 cm.
e) What is the speed of the fastest of the three when it reaches the floor?
3.96 m/s.
f) What is the speed of the slowest of the three when it reaches the floor?
0.37 m/s.