1.
This question is about the kinematics of an elevator (lift).
(a)
Explain the difference between the gravitational mass and the inertial mass of an object.
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(3)
An elevator (lift) starts from rest on the ground floor and comes to rest at a higher floor. Its
motion is controlled by an electric motor. A simplified graph of the variation of the elevator’s
velocity with time is shown below.
(b)
The mass of the elevator is 250 kg. Use this information to calculate
(i)
the acceleration of the elevator during the first 0.50 s.
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(2)
(ii)
the total distance travelled by the elevator.
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(2)
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(iii)
the minimum work required to raise the elevator to the higher floor.
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(2)
(iv)
the minimum average power required to raise the elevator to the higher floor.
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(2)
(v)
the efficiency of the electric motor that lifts the elevator, given that the input power
to the motor is 5.0 kW.
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(2)
(c)
On the graph axes below, sketch a realistic variation of velocity for the elevator. Explain
your reasoning. (The simplified version is shown as a dotted line)
(2)
2
The elevator is supported by a cable. The diagram below is a free-body force diagram for when
the elevator is moving upwards during the first 0.50 s.
(d)
In the space below, draw free-body force diagrams for the elevator during the following
time intervals.
(i)
0.5 to 11.50 s
(ii)
11.50 to 12.00 s
(3)
A person is standing on weighing scales in the elevator. Before the elevator rises, the reading on
the scales is W.
(e)
On the axes below, sketch a graph to show how the reading on the scales varies during the
whole 12.00 s upward journey of the elevator. (Note that this is a sketch graph – you do
not need to add any values.)
(3)
3
(f)
The elevator now returns to the ground floor where it comes to rest. Describe and explain
the energy changes that take place during the whole up and down journey.
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(4)
(Total 25 marks)
2.
This question is about projectile motion.
A marble is projected horizontally from the edge of a wall 1.8 m high with an initial speed V.
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A series of flash photographs are taken of the marble. The photographs are combined into a
single photograph as shown below. The images of the marble are superimposed on a grid that
shows the horizontal distance x and vertical distance y travelled by the marble.
The time interval between each image of the marble is 0.10 s.
(a)
On the images of the marble at x = 0.50 m and x = 1.0 m, draw arrows to represent the
horizontal velocity VH and vertical velocity VV.
(2)
(b)
On the photograph, draw a suitable line to determine the horizontal distance d from the
base of the wall to the point where the marble hits the ground. Explain your reasoning.
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(3)
(c)
Use data from the photograph to calculate a value of the acceleration of free fall.
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(3)
(Total 8 marks)
5
3.
This question is about linear motion.
A police car P is stationary by the side of a road. A car S, exceeding the speed limit, passes the
police car P at a constant speed of 18 m s–1. The police car P sets off to catch car S just as car S
passes the police car P. Car P accelerates at 4.5 m s–2 for a time of 6.0 s and then continues at
constant speed. Car P takes a time t seconds to draw level with car S.
(a)
(i)
State an expression, in terms of t, for the distance car S travels in t seconds.
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(1)
(ii)
Calculate the distance travelled by the police car P during the first 6.0 seconds of its
motion.
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(1)
(iii)
Calculate the speed of the police car P after it has completed its acceleration.
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(1)
(iv)
State an expression, in terms of t, for the distance travelled by the police car P
during the time that it is travelling at constant speed.
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(1)
(b)
Using your answers to (a), determine the total time t taken for the police car P to draw
level with car S.
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(2)
(Total 6 marks)
6
4.
Linear motion
At a sports event, a skier descends a slope AB. At B there is a dip BC of width 12 m. The slope
and dip are shown in the diagram below. The vertical height of the slope is 41 m.
A
(not to scale)
slope
41m
C
B
D
1.8m
dip
12m
The graph below shows the variation with time t of the speed v down the slope of the skier.
25.0
20.0
15.0
v / ms –1
10.0
5.0
0.0
0.0
1.0
2.0
3.0
4.0 5.0
t/s
6.0
7.0
8.0
The skier, of mass 72 kg, takes 8.0 s to ski, from rest, down the length AB of the slope.
(a)
Use the graph to
(i)
calculate the kinetic energy EK of the skier at point B.
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(2)
(ii)
determine the length of the slope.
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(4)
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(b)
(i)
Calculate the magnitude of the change EP in the gravitational potential energy of
the skier between point A and point B.
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(2)
(ii)
Use your anwers to (a)(i) and (b)(i) to determine the ratio
EP  EK  .
EP
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(2)
(iii)
Suggest what this ration represents.
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(1)
(c)
At point B of the slope, the skier leaves the ground. He “flies” across the dip and lands on
the lower side at point D. The lower side C of the dip is 1.8 m below the upper side B.
(i)
Calculate the time taken for an object to fall, from rest, through a vertical distance
of 1.8 m. Assume negligible air resistance.
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(2)
(ii)
The time calculated in (c)(i) is the time of flight of the skier across the dip.
Determine the horizontal distance travelled by the skier during this time, assuming
that the skier has the constant speed at which he leaves the slope at B.
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(2)
(Total 15 marks)
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10
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12
This question is about projectile motion.
A marble is projected horizontally from the edge of a wall 1.8 m high with an initial speed V.
A series of flash photographs are taken of the
marble. The photographs are combined into a
single photograph as shown below. The images of
the marble are superimposed on a grid that shows
the horizontal distance x and vertical distance y
travelled by the marble.
V
1.8 m
ground
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The time interval between each image of the marble is 0.10 s.
0
(a)
0.50
x/m
1.0
1.5
2.0
0
On the images of the marble at x =
0.50 m and x = 1.0 m, draw arrows
to represent the horizontal velocity
VH and vertical velocity VV.
–0.50
y/m
–1.0
–1.5
(2)
(a)
–2.0
0
0.50
x/m
1.0
1.5
2.0
0
–0.50
y/m
–1.0
–1.5
–2.0
Mark both together.
VH : horizontal arrows equal in length;
VV : two vertical arrows, the one at 1.0 m noticeably longer than the one at 0.5 m;2
If arrows correct but wrong point(s) award [1].
(b)
On the photograph, draw a suitable line to determine the horizontal distance d from the
base of the wall to the point where the marble hits the ground. Explain your reasoning.
(b)
curve that goes through all data points;
stops at y = 1.8m as this is the height of the wall;
from graph d = 1.5(± 0.1)m;
(3)
(c)
Use data from the photograph to calculate a value of the acceleration of free fall.
(c)
travels vertically 1.8m in 0.6s / 1.25m in 0.5s;
2s
g= 2 ;
t
to give g = 10 (±1) m s–2; 3
Award [2 max] for any time shorter than 0.5 s.
(3)
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