Download PHYS 243, Exam 1

Here are some statistics on the grades for exam 1:
Grades on the first exam ranged from a high of 105 down to a low of 15. (The maximum
possible grade was 110.) In the 930 section the average grade was 56.0 + 22.2. In the
1030 section the average grade was 59.6 + 21.7. (The meaning of the + the range that
includes 68% of the grades, so 16% got outside this range on the low side and 16% got
outside this range on the high side.)
I also looked at grades based on whether people were in the Wed or Fri recitations, and
here are the results. For Fri recitations the average grade was 56.3, which was not
much lower than for Wed recitations – 59.5. Also, the Friday recitations had more
people with grades of 90 or above (13) than did the Wednesday recitations (10). Based
on these comparisons there is no real evidence that people in the Friday recitations
were significantly hurt by missing last week’s recitation.
Here are the solutions to the exam:
Problem 1. A block of mass m = 2 kg resting on a rough horizontal surface is pushed by a force F = 10
Newtons that acts along a direction 37 degrees below the horizontal as shown. The block moves at a
constant velocity v = 5 m/s.
(a) (8 pts) What is the net force on the block? ANSWER: F_net = 0, since a = 0
(b) (8 pts) What is the magnitude of the friction force that acts on the block?
Fx  F cos  f  max  0
Thus, 10 cos 37  f  0 so that f  10 cos 37  8.0 N
(c) (8 pts) If the block were accelerating with a = +1 m/s^2 instead of travelling at constant velocity,
what would the friction force have to be? (Assume no change in the applied force F or the mass of the
block.)
Fx  F cos   f  max so that: f  10 cos 37  max  8.0  2(1)  6.0 N
(some versions of the test had other values for the acceleration a.)
(d) (11 pts) What is the coefficient of sliding or kinetic friction  k given the assumptions in (c)?
First find the normal force N, using: Fy  N  F sin   mg  ma y  0 , which yields
N  10 sin 37  mg  6.0  2(9.8)  25.6 N .
In part (d) it was shown that f = 6.0 N, therefore, we have:
k 
f
6.0

 0.23
N 25.6
some versions of the test had a different order of the questions.
______1. How many m/s is 50 mi/hr equivalent to? ( 1 mi = 1609 m)
(a) 49 m/s
(b) 2.2 m/s
(c) 22 m/s
(d) 45 m/s
them
(e) none of
______2. A motorist travels for 3.0 h at 80 km/h and then 2.0 h at 100 km/h. What is her average speed
for the 5 hrs?
(a) 85 km/h
them
(b) 88 km/h
(c) 90 km/h
(d) 92 km/h
(e) none of
______3. Starting from city A, a car drives 250 mi east to city B, then 300 mi north to city C, and
finally 700 mi west to city D. The distance between city A & D is (a) 350 mi
(b) 460 mi
(c) 570 mi
(d) 680 mi
(e) none of them
(C was counted as correct because it is not that far from the correct answer 540 mi.)
______4. An object moving in the +x-direction experiences an acceleration of 2.0 m/s^2. It is
therefore:
(a) travelling 2.0 m each second
(b) travelling 5.0 m/s each second
(c) changing its velocity by 5.0 m/s
(d) increasing its velocity by 2.0 m/s each second
______5. A stone is thrown off a high cliff with an initial velocity that makes an angle 45 degrees
above the horizontal, so that the x and y components of the initial velocity are both 2.0 m/s. After the
stone is in the air for 5 seconds, the x and y components of its velocity are:
(a) 2.0 m/s, - 49.0 m/s
(b) 2.0 m/s, - 47.0 m/s
(c) 49.0 m/s, - 49 m/s (d) 49.0 m/s, 47.0 m/s
______ 6. While a nail is hammered into a board, the magnitude of the force of the nail on the board
_______ the force of the board back on the nail.
(a) equals
(b) exceeds
(c) is less than
(d) is twice
_______7. When a wind blows towards the east, a plane heading due north winds up travelling 10
degrees east of north due to the wind. The wind speed divided by the plane’s air speed (speed relative
to the air) is therefore given by the _______ of 10 degrees.
(a) sine (b) cosine
(c) tangent
(d) cotangent
_______8. Newton’s First Law is true:
(a) in all circumstances
(b) only in inertial reference frames
(c) only in noninertial reference frames
(d) only in reference frames that are at rest
_______9. The velocity versus time graph for a moving object is a straight line whose slope is negative
and it crosses the t-axis at 5.0 sec. We can conclude that the object’s _____ is negative, and its velocity
is ___ at times greater than 5.0 sec.
(a) velocity, positive (b) velocity, negative (c) acceleration, positive (d) acceleration, negative
_______10. A car travels 100 mi due north at constant speed, and then turns back and goes halfway
back to its starting point at the same speed. The average speed of the car would be ____ times its
average velocity.
(a) one
(b) two
(c) three
(d) four
(e) none of them
________11. A cart with an initial velocity of 5.0 m/s experiences an acceleration of 2.0 m/s^2. What
is the cart’s displacement during the first 6.0 s of its motion? (a) 10 m
(b) 55 m
(c) 66 m
(d) 80 m
________12. A ball is thrown straight up. Just before reaching its highest point the magnitude of its
acceleration is
(a) zero
(b) slightly less than g
(c) g
(d) slightly more than g
________13. A football is kicked from ground level and lands at ground level after travelling 200 ft
horizontally. If the football were kicked with half its original velocity, but along the same initial
direction, how far would it travel horizontally? (a) 25 ft
(b) 50 ft
(c) 100 ft
(d) 150 ft
________14. Bonus question (for extra 5 points): My office hours are on MWF at the following times:
(a) 8:30 – 9:30
(b) 11:30-12:30
(c) 12:30-1:30
(d) 2:30 – 3:30