101
Second Physics Midterm Exam
Spring 2007-2008 Saturday, May 10, 2008 9:00 a.m. 11:00 a.m.
Students Name:
.
Students Number: . Choose your Instructors Name : Prof. Fekri El-Akkad. Dr. Ahmed Ali Al-Jassar Dr. Hala K. Al-Jassar Dr. Abdel Mohsen Habib Dr. Tarek Al Refaey Grades: Dr. Hasan Rafaat Dr. Adnan Al-Yaseen Dr. Ismail Sabbah Dr. Ashraf Zaher Dr. Tarek Ramadan
Problems Points
Q1
Q2
Q3
Q4
P1
P2
P3
P4
P5
P6
P7
P8
Total
Important Notes: 1. 2. 3. 4. 5. 6. 7. 8. 9. The exam contains 4 questions and 8 problems in 3 pages plus the front page. Answer all questions and problems. Each question will be assigned 1 point. Each problem will be assigned 2 points. No solution for problems = no points. Check the correct answer for each question. Take g = 10 m/s2 Mobiles and Pagers are not allowed during the exam. Programmable calculators which can store equations are not allowed.
GOOD LUCK
Kuwait University Science College Physics Dept. PHYS101
Fall 2007 (10-May-08)
Part I: Questions
Choose the correct answer
F
1. Two masses M and m (<M) are connected by a string. We would like to raise them up at constant speed by a force F. Then, the tension in the string between the two masses will be (a) Ta = Tb = 0 (b) Ta < Tb (c) Ta = Tb (d) Ta > Tb
F m M Tb m m M
Ta M
2. A mass m is placed on top of a mass M and the system accelerates on a rough horizontal surface under the action of a force F acting on M as shown in the figure. If the mass m is on the verge of slipping, then the frictional force exerted on it equals (a) s mg (b) k mg (c) s (m+M)g (d) k (m+M)g
F
C B
h
3. A block initially released from rest at a height h above the ground moves along a frictionless surface. If the hills have identical circular tops with different heights, as shown, then on which hill top will the normal force exerted on the block be maximum (a) A (b) B (c) C (d) A and B
A
4. An object moves a distance d along the rough incline shown. the magnitude of the work done by the frictional force is (a) k mgh Part II: Problems (b) k mgd (c) k mgL
m d L h
(d) 0
Solve the following problems
1. A 5-kg block is moving in the positive x-direction while a net horizontal force F of 30 N is acting on it in the negative x-direction. If the initial velocity of the block is 8 m/s calculate its velocity (in m/s) after 4.0 s.
a=
F 30 = = 6 m / s 2 5 m
v = v0 + at = 8 + ( 6 )(4 ) = 8 24 = 16 m / s
2. An elevator moves with a constant speed vertically upward a distance of 8 m in 5 seconds. It is driven by a motor that provides a maximum power of 40 hp. Find the maximum overall weight (in N) of the elevator with the passengers. (Hint: 1 hp = 746 W) Since the motion is in a straight at line constant speed thus, Fmotor W = 0
Fmotor = W
v = 8 5 = 1.6 m / s Pmotor = Fmotor v
W= Pmotor (40 )(746 ) = = 18650 N v 1.6
p.1/3
Kuwait University Science College Physics Dept. PHYS101
Fall 2007 (10-May-08)
3. A block of mass 2.0 kg rests on a rough 45o incline with coefficient of kinetic friction k=0.5. What force F (in N) must be exerted in the horizontal direction, to move the block with a constant speed in the upward direction along the incline? .
F cos f k mg sin = 0 F
f k = k N N = F sin + mg cos F cos k (F sin + mg cos ) mg sin = 0 F=
45o
( k + tan ) mg = (3)(20 ) = 60 N (1 k tan )
4. The seat of a swing is connected to two cables as shown in the figure, one of which is horizontal. It rotates with a person sitting on it in a horizontal circle at a speed of 10 m/s. If the overall mass of the seat and the person is 70 kg, find the tension (in N) in the horizontal cable.
T1 + T2 sin = m T2 cos = mg T1 = m
V2 R
45o
V2 mg tan R
7m
100 T1 = (70 ) (70 )(10 )(1) = 300 N 7
5. A single variable force F acts on a 0.1-kg mass as it moves along the x-axis. The force varies with position as shown in the figure. The speed of the mass at x=4 m is 5 m/s. What is its speed (in m/s) at x=8 m?
1 1 WF = (8 )(10 ) (4 )(5 ) = 30 J 2 2 WF = v2 = 1 2 m v 2 v0 2
F (N)
10
(
)
5
2WF 60 2 + v0 = + (25 ) = 625 m 0.1
v = 625 = 25m / s
0
4
8
12
x (m)
p.2/3
Kuwait University Science College Physics Dept. PHYS101
Fall 2007 (10-May-08)
6. A 2.0-kg block is pushed against a spring with a spring constant k = 500 N/m, compressing it 0.30 m. When the block is released, it moves along a frictionless 30.0o incline. How far (in m) does the block travel up the incline before starting to slide back down?
Ei = E f
12 kx = mgh 2
kx 2 (500 )(0.09 ) = 1.125m h= = 2mg 2(2 )(10 )
d= h = 2.25 m sin
30o
7. Consider the system shown in the figure. The coefficient of kinetic friction between the 8.00kg block and the tabletop is k=0.3. The blocks are released from rest. Calculate the kinetic energy (in J) of the 4.00-kg block after it has descended 1.5 m. 8 kg
E f = Ei + W f
1 (m + M )v 2 = mgh + W f 2
W f = k Mgh
v=
K=
2(mgh + W f
(m + M )
)
-2
4 kg
= 2m / s
1 (4 )(4 ) = 8 J mv 2 = 2 2
8. A particle is moving along the x-axis under the action of a variable conservative force. The potential energy (in Joules) associated with this force is given by U ( x ) = 2 x 2 4 x + 6 , where x is in meters. When the force acting on the particle is zero its kinetic energy is 32 J. Find the mechanical energy (in J) of the particle.
dU = 4 x + 4 dx
x = 1m
F =
F =0
U (1m ) = 2 4 + 6 = 4 J E = U (1m ) + K (1m) = 4 + 32 = 36 J
p.3/3