MAKE-UP Test #4
1. (4 pts) You are standing at the edge of a cliff 20 m high, and you kick a soccer ball
horizontally with an initial speed of 20 m/s.
(a) How much time does it take for the ball to hit the ground?
Ans: 12 gt2 = 20 m ⇒ t2 = 2 × 20 m/(10 m/s2 ) ⇒ t = 2 s
(b) How far from the base of the cliff does the ball land?
Ans: 20 m/s × 2 s = 40 m
2. (2 pts) A new planet has been discovered that has twice the mass of the Earth and
has a radius twice the radius of the Earth. What is the acceleration of gravity (i.e. g)
on the surface of this new planet?
2
Ans: gEarth = GME /RE
, so for the new planet gnew = G(2ME )/(2RE )2 =
1
2
) = 5 m/s2 .
× (GME /RE
2
3. (4 pts) A block of mass 4 kg slides on a tabletop with no friction at a speed 3 m/s
until it bangs into and sticks to a second block of mass 2 kg which was initially at rest.
Together they continue to slide with a common speed vf .
(a) What is the common speed vf of the masses after the collision? Be certain to
include the appropriate units on your answer.
Ans: Use the conservation of momentum. pi = 4 kg × 3 m/s = pf = (4 kg +
2 kg)vf ⇒ vf = 2 m/s.
(b) How much kinetic energy was lost in the collision? Be certain to include the
appropriate units on your answer.
Ans: K.E.i = 21 × 4 kg × (3 m/s)2 = 18 J, and K.E.f =
so 6 J were lost in the collision.
1
1
2
× 6 kg × 4( m/s)2 = 12 J
4. (4 pts) A large, heavy rock has a mass of 90 kg and a density three times the density
of water. A rope is tied around the rock, and the rock is then lowered until it is 5 m
below the surface of the water.
(a) What is the weight (not mass! ) of an amount of water which has the same volume
as the rock?
Ans: Water has 1/3 the density of the rock, so the weight of the water is 1/3 the
weight of the rock, or (90 kg × 10 m/s2 )/3 = 300 N. This is also the buoyant force
acting on the rock.
(b) What is the tension in the rope? NOTE: Tension is a force, not a mass.
Ans: The buoyant force on the rock is the weight of the displaced water. The
buoyant force is 300 N so she tension in the rope is T = 900 N − 300 N = 600 N.
5. (2 pts) The ends of a 50 Volt battery are attached to two separate metal plates 1 cm
apart, each with an area of 10 cm2 . The two plates are parallel with one above the
other as shown in the diagram. A small ball bearing, about 1mm in diameter, has
1Coulomb of positive charge on it, and you are holding it very close to the negatively
charged metal plate.
(a) How much energy would you have to provide in order to move the ball bearing
to the positively charged plate?
Ans: 1 C × 50 V = 1000 J.
(b) Is this energy positive or negative?
Ans: Positive
6. (2 pts) A two meter long see-saw is balanced on a fulcrum in the middle. A girl of
mass 40 kg sits at one end of the see-saw. A boy of mass 50 kg sits on the other side
of the see-saw to balance the see-saw. How far is the boy from the fulcrum?
Ans: 0.8 m
2
7. (4 pts) You have three objects of identical mass and radius that will roll down an
inclined plane. Mass A is a uniform solid cylinder. Mass B is a hoop—all of the mass
is distributed along the outer rim of the object. Mass C is concentrated at the center
of the object with just very little mass going around the rim—this looks somewhat
like a bicycle wheel.
(a) If a race were held rolling all three objects down a ramp, which object would be
the first one down the ramp?
Ans: object C
(b) Which object would be last down the ramp?
Ans: object A
8. (2 pts) A spool with a pink ribbon around it is on the front desktop. If the ribbon is
pulled gently to the right, and if the spool rolls without slipping, it will
(Circle your answer.)
(a)
(b)
(c)
(d)
move to the left.
stay in the same place.
move to the right.
lift off the table.
9. (4 pts) At the front of the classroom is a large water-filled jar, on a turntable, with
an orange ball tied to a string that keeps it from floating to the top, and a blue ball
that is tied to a string that keeps it from sinking to the bottom. When the turntable
is spun ...
(a) Does the orange ball move out or in?
Ans: in
(b) Does the blue ball move out or in?
Ans: out
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