PC 141/PC161, Dr. Maher Ahmed, closed book exam, 10 questions, the calculator is allowed
Question 1
You throw a stone vertically upward with an initial speed of 10 m/s from a thirdstory office window. If the window is 10m above the ground, find the total time the
stone will take to reach the ground.
-10=10t-0.5*9.8*t2
𝑡=
−10±√102 +4∗4.9∗10
−2∗4.9
= 2.78 𝑠𝑒𝑐
Question 2
Ilya can run at a speed of 6m/s and walk at a speed of 2m/s .On a route of length 8 m. Ilya walks
half of the time and runs the other half. How long does it take Ilya to cover the distance of 8 m.
(6*t/2)+(2*t/2)=8
8t=16
t=2 sec
Question 3
A stone thrown off a bridge 20 m above a river has an initial velocity 14.14 m/s at an angle of
45o above the horizontal. What is the range R of the stone?
V=14.14cos45 x+ 14.14 sin45 y=10 x +10 y
Y=10t-0.5*9.8t2, -20=10t-4.9t2 𝑡 =
−10±√102 +4∗4.9∗20
−2∗4.9
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= 3.28 𝑠𝑒𝑐, R=10*3.28=32.8 m
PC 141/PC161, Dr. Maher Ahmed, closed book exam, 10 questions, the calculator is allowed
Question 4
A stone thrown off a bridge 20 m above a river has an initial velocity 14.14 m/s at an angle of
45o below the horizontal. What is the range R of the stone?
V=14.14cos45 x - 14.14 sin45 y= 10 x -10 y
Y=-10t-0.5*9.8t2, -20=-10t-4.9t2 𝑡 =
10±√102 +4∗4.9∗20
−2∗4.9
= 1.24 𝑠𝑒𝑐, R=10*1.24=12.4 m
Question 5
In the figure shown below m1 = 141.4kg and m2 = 20kg. Neglect the friction between m1 and
the table. After the system begins to move, what is the magnitude and direction of the
acceleration? What is the tension force in the robe?
T-m2g=m2a, m1*sin(45)-T=m1a
a=(100-20)*9.8/161.4= 4.86 m/sec2 in the direction of m1
T=m2(g+a)=20*(9.8+4.9)=294N
Question 6
A 1 kg mass is placed on the end of a spring that has a spring constant of 100 N/m. The mass–
spring system rests on a frictionless incline that is at an angle of 30o from the horizontal. The
system is eased into its equilibrium position, where it stays. Determine the change in elastic
potential energy of the system.
F=kx=m*g*sin(30), x=mg/2*100, U=(1/2)*k*x2=m2*g2/8k=1*9.8*9.8/800=0.12 Joul
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PC 141/PC161, Dr. Maher Ahmed, closed book exam, 10 questions, the calculator is allowed
Question 7
A 0.030 Kg bullet with a speed of 500 m/s strikes a target brick of mass 1.0 kg. The brick breaks
into two fragments. The bullet deflects at an angle of 30o above the + x axis and has a reduced
speed of 100 m/s. One piece of the brick (0.75 kg) goes off to the right as shown below with
speed 5 m/s. Determine the speed and direction of the other piece of the brick immediately after
the collision.
mbV0=mbVb+m1V1+m2V2
mbV0=mbVbcos30+m1V1+m2V2cos 𝜃2
𝑣2 cos 𝜃2 =
0.03∗500−0.03∗100∗0.866−0.75∗5
0.25
mbVb sin30=m2V2sin Ɵ2, 𝑣2 sin 𝜃2 =
=
15−2.598−3.75
0.03∗100∗0.5
0.25
0.25
= 34.608
1.5
= 0.25 = 6
Tan𝜃2 =0.17 𝜃2 = 9.8 𝑑𝑒𝑔𝑟𝑒𝑒𝑠, 𝑣2 = 35.25𝑚/𝑠
Question 8
Three masses 2.0 kg, 3.0 kg and 5.0 kg are located at positions (3.0, 0), (6.0,0), and (-4.0, 0),
respectively, in meters from the origin where is the center of mass of this system?
Xm=((2*3)+(3*6)+(5*-4))/10=0.4m
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PC 141/PC161, Dr. Maher Ahmed, closed book exam, 10 questions, the calculator is allowed
Question 9
A microwave oven has 0.30 m diameter plate for oven cooking. The plate accelerates from rest at
uniform rate of 0.87 rad/s2 for 0.5 s before reaching its constant operational speed. (a) How many
revolutions does the plate make before reaching its operational speed? (b) What are the
operational angular speed of the plate and the operational tangential speed at its rim?
The angle= 0+0.5*0.87*0.5*0.5=0.11 rad
=0.017 rev
ω=0+0.87*0.5=0.44 rad/s
rω=0.15*0.44=0.066 m/s
Question 10
A picture hangs motionless on a wall. If the picture has a mass of 3.0 kg, what are the
magnitudes of the tension forces in the wires?
(T1+T2)/1.41=3*9.8
T1=T2
T1=3*9.8*1.41/2=21.18 N
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