Download Midterm I Physics 231

FORM A
Midterm I Physics 231
October 6th, 2010
Solutions
1. A rectangle has length 3.24 m and height 53.2 cm. What is the area of the
rectangle?
a) 172.37 m2
b) 1.723 m2
c) 172.4 cm2
d) 1.72 m2
Area=length x height = 3.24 x 0.532 = 1.72 m2 (note only 3 significant figures)
2. John walks 1.00 km north, then turns right and walks 1.00 km east. His speed is 1.5
m/s during the entire stroll. If Jane starts walking at the same time and place as John,
but in a straight line to the endpoint, at what speed should she walk to arrive at the
endpoint just when John does? Hint: draw a diagram of the trajectories.
a) 2.8 m/s
b) 5.7 m/s
c) 1.5 m/s
d) 1.1 m/s
John: d1=v1t thus 2000=1.5t which means t=1333 s. Jane follows the hypotenuse of
the triangle d2=(10002+10002)=1414 m. then v2=d2/t= 1.1 m/s (only 2 significant
figures)
3.The velocity-versus-time for three drag racers are shown in the figure below. At
t=5.0 s which car has travelled the furthest?
a) Andy’s car
b) Betty’s car
c) Carl’s car
d) All travelled the same distance
Andy
5.0 s
Betty
5.0 s
Carl
5.0 s
Displacement is the area under the graph v(t). therefore Betty’s car travelled the
furthest since the area under her graphs is larger.
4. A car is travelling at vx=20 m/s. The driver applies the breaks, and the car slows
with an acceleration of ax=-4.0 m/s2. What is the distance travelled until it stops?
a) 20 m
b) 100 m
c) 50 m
d) -80 m
Motion with constant acceleration: v=v0-at and x=v0t -½at2;
From the first equation we obtain the time: 0=20-4t; t=5 s
Using the second equation we determine the displacement x=205 – 0.5452=50 m
5. A student at the top of a building of height h throws ball A straight upward with
speed v0 and throws ball B straight downward with the same initial speed. Which of
the following statements referring to the free fall motion is correct?
a) The acceleration on ball A is the same as on ball B.
b) The speed of ball A when it hits the ground is larger than the speed of ball B
when it hits the ground.
c) The time ball A takes to reach the ground is the same as the time it takes for
ball B to hit the ground.
d) The acceleration on ball A is equal in magnitude but opposite in sign as the
acceleration of ball B.
The first statement is correct. All free falling objects at the surface of the earth are
subject to the same gravitational acceleration. Answer b) is not correct because both
speeds are the same when the balls hit the ground since they start from the same
height – same initial potential energy. Ball A will necessarily take longer to hit the
ground than B.
6. A plane has an air speed of 200 mph. The pilot wishes to reach a destination 600 mi
due east, but the wind is blowing at 50 mph to the north. In what direction must the
pilot head the plane in order to reach her destination?
a) The pilot should follow the direction 4.80 south of east.
b) The pilot should follow the direction 140 south of east.
c) The pilot should follow the direction 4.80 north of east.
d) The pilot should follow the direction 140 north of east.
In order for the plane to move east, the pilot needs to direct the plane such that its
velocity along north-south cancels the wind’s speed. As the plane has a speed of
v(plane-air)=200 mph then sin(theta)=50/200 and thus theta=14 degrees south of east

50
200
7. A ball is fired from a canon at ground level with an initial speed of 10 m/s, at an
angle of 600 with the horizontal direction. The ball follows a parabolic trajectory
where air resistance can be neglected. Which of the following statements is correct?
a) The velocity of the ball at the point of maximum height is zero.
b) The acceleration of the ball at the point of maximum height is zero.
c) The displacement of the ball depends of the mass of the ball.
d) The time the ball takes to reach the point of maximum height is 0.88 s.
Answer a) is not correct since the ball still has velocity in the horizontal direction. The
acceleration is always g therefore b) is not correct. The displacement is not dependent
on the mass, so c) is incorrect. So the correct solution must be d). Let us verify.
The time to reach the top can be determined from the velocity equation in the vertical
direction since that component becomes zero at the point of maximum height.
vy=v0-gt which gives 0=10 sin60 – 9.8 t ; t=0.88s
8. Block A is sitting on top of block B. A constant force is exerted on block B,
causing it to accelerate to the right. Block A rides on block B without slipping. Which
statement is true?
a) Block B exerts a friction force on block A, directed to the left.
b) Block B exerts a friction force on block A, directed to
the right.
c) Block B does not exert a friction force on block A.
d) None of the above
A
B
Block A moves to the right with B, therefore since the only force acting on A in the
horizontal direction is the friction force, it has to be to the right. Also note that block
A exerts a frictional force on B which is pointing towards the left. Since Newton 3rd
law states that FAB=-FBA, the force of B on A must point to the right.
9. A demo pendulum is hanging from the ceiling of a classroom and has length 2.5 m.
The ball at the end of the pendulum has mass 5.0 kg and is released with an initial
velocity v0 with the rope making an angle with the vertical axis of =300. Determine
the minimum initial speed needed for the ball to touch the ceiling in its swing.
a) 42.4 m/s.
b) 7.0 m/s
c) 6.5 m/s
d) 4.9 m/s
ceiling

Let us define initial potential energy as our reference zero. This means that initially,
the ball only have kinetic energy. After it reaches the ceiling it only has gravitional
potential energy: ½ mv2=mgLcos(); v0= (2gLcos()); v0=(29.82.5cos(30))=6.5
m/s
10. Two blocks of masses M1 and M2 are connected as illustrated in the figure below.
Ignoring the mass of the pulley, knowing that M1>M2 and that M2 is moving with
constant velocity, which of the following statements is correct?
a) The tension in the string acting on M1 is larger than that acting on M2
b) The magnitude of the gravitational force on M1 equals
the tension of the string on M1.
c) There is a non-zero net force acting on M2
d) The magnitude of the normal force on M2 is larger than that of the total
gravitational force acting on M2
If the blocks move with constant speed this means that there is not net force on either
M1 or M2. Answer b) is correct since these are the only two forces on M1 and they
have to cancel each other.
11. A hockey puck with mass 100 g, sliding along frictionless ice with a speed 2.0 m/s
to the right, runs into a spring and compresses it by 2.0 cm before coming to a
momentary stop. What is the elastic constant of the spring K?
a) 0.1 N/m
b) 49 N/m
c) 100 N/m
d) 1000 N/m
Conservation of energy, namely transformation of kinetic energy into elastic potential
energy: ½mv2= ½Kx2; K=mv2/x2=0.1 x 22/(0.02)2=1000 N/m.