XI-Physics-Force with Graph
2
A sky-diver jumps from a high-altitude balloon.
(a) Explain briefly why the acceleration of the sky-diver
(i)
decreases with time,
..................................................................................................................................
..................................................................................................................................
............................................................................................................................ [2]
is 9.8 m s–2 at the start of the jump.
(ii)
..................................................................................................................................
............................................................................................................................ [1]
(b) The variation with time t of the vertical speed v of the sky-diver is shown in Fig. 2.1.
40
v / m s–1
30
20
10
0
0
2
4
6
8
10
12
Fig. 2.1
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14
16
18
20
22
24
26
t/s
28
2
Use Fig. 2.1 to determine the magnitude of the acceleration of the sky-diver at time
t = 6.0 s.
acceleration = ..................................... m s–2 [3]
(c) The sky-diver and his equipment have a total mass of 90 kg.
(i)
Calculate, for the sky-diver and his equipment,
1. the total weight,
weight = ........................................... N [1]
2. the accelerating force at time t = 6.0 s.
force = ........................................... N [1]
(ii)
Use your answers in (i) to determine the total resistive force acting on the sky-diver
at time t = 6.0 s.
force = ........................................... N [1]
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1
(a) (i)
Define acceleration.
..................................................................................................................................
............................................................................................................................. [1]
(ii)
State Newton’s first law of motion.
..................................................................................................................................
............................................................................................................................. [1]
(b) The variation with time t of vertical speed v of a parachutist falling from an aircraft is
shown in Fig. 1.1.
60
B
50
C
v / m s–1
40
30
D
20
10
E
0
A
0
10
20
30
t /s
Fig. 1.1
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(i)
Calculate the distance travelled by the parachutist in the first 3.0 s of the motion.
distance = ............................................ m [2]
(ii)
Explain the variation of the resultant force acting on the parachutist from t = 0
(point A) to t = 15 s (point C).
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
............................................................................................................................. [3]
(iii)
Describe the changes to the frictional force on the parachutist
1. at t = 15 s (point C),
..................................................................................................................................
..................................................................................................................................
............................................................................................................................. [1]
2. between t = 15 s (point C) and t = 22 s (point E).
..................................................................................................................................
..................................................................................................................................
............................................................................................................................. [1]
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3
(a) State Newton’s first law of motion.
...................................................................................................................................................
.............................................................................................................................................. [1]
(b) A box slides down a slope, as shown in Fig. 3.1.
v
box
20°
horizontal
Fig. 3.1
The angle of the slope to the horizontal is 20°. The box has a mass of 65 kg. The total resistive
force R acting on the box is constant as it slides down the slope.
(i)
State the names and directions of the other two forces acting on the box.
1. ........................................................................................................................................
2. ........................................................................................................................................
[2]
(ii)
The variation with time t of the velocity v of the box as it moves down the slope is shown
in Fig. 3.2.
8.0
6.0
v / m s–1
4.0
2.0
0
0
1.0
Fig. 3.2
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t /s
2.0
6
1. Use data from Fig. 3.2 to show that the acceleration of the box is 2.6 m s–2.
[2]
2. Calculate the resultant force on the box.
resultant force = ...................................................... N [1]
3. Determine the resistive force R on the box.
R = ...................................................... N [3]
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2
(a) State the two conditions for a system to be in equilibrium.
1. ...............................................................................................................................................
...................................................................................................................................................
2. ...............................................................................................................................................
...................................................................................................................................................
[2]
(b) A paraglider P of mass 95 kg is pulled by a wire attached to a boat, as shown in Fig. 2.1.
parachute
paraglider
P
wire
boat
25°
horizontal
water
Fig. 2.1
The wire makes an angle of 25° with the horizontal water surface. P moves in a straight line
parallel to the surface of the water.
The variation with time t of the velocity v of P is shown in Fig. 2.2.
10.0
8.0
v / m s–1
6.0
4.0
2.0
0
0
2.0
4.0
Fig. 2.2
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6.0
t /s
8.0
8
(i)
Show that the acceleration of P is 1.4 m s–2 at time t = 5.0 s.
[2]
(ii)
Calculate the total distance moved by P from time t = 0 to t = 7.0 s.
distance = .......................................................m [2]
(iii)
Calculate the change in kinetic energy of P from time t = 0 to t = 7.0 s.
change in kinetic energy = ........................................................ J [2]
(iv)
The tension in the wire at time t = 5.0 s is 280 N.
Calculate, for the horizontal motion,
1. the vertical lift force F supporting P,
F = ....................................................... N [3]
2. the force R due to air resistance acting on P in the horizontal direction.
R = ....................................................... N [3]
[Total: 14]
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3
A steel ball falls from a platform on a tower to the ground below, as shown in Fig. 3.1.
platform
tower
ball
path of
ball
192 m
ground
Fig. 3.1
The ball falls from rest through a vertical distance of 192 m. The mass of the ball is 270 g.
(a) Assume air resistance is negligible.
(i)
Calculate
1.
the time taken for the ball to fall to the ground,
time taken = ........................................................s [2]
2.
the maximum kinetic energy of the ball.
maximum kinetic energy = ........................................................J [2]
(ii)
State and explain the variation of the velocity of the ball with time as the ball falls to the
ground.
...........................................................................................................................................
.......................................................................................................................................[1]
(iii)
Show that the velocity of the ball on reaching the ground is approximately 60 m s–1.
[1]
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(b) In practice, air resistance is not negligible. The variation of the air resistance R with the
velocity v of the ball is shown in Fig. 3.2.
4.0
3.0
R/N
2.0
1.0
0
0
20
40
60
80
v / m s–1
100
Fig. 3.2
(i)
Use Fig. 3.2 to state and explain qualitatively the variation of the acceleration of the ball
with the distance fallen by the ball.
...........................................................................................................................................
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[3]
(ii)
The speed of the ball reaches 40 m s–1. Calculate its acceleration at this speed.
acceleration = ................................................. m s–2 [2]
(iii)
Use information from (a)(iii) and Fig. 3.2 to state and explain whether the ball reaches
terminal velocity.
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
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4
A trolley moves down a slope, as shown in Fig. 4.1.
trolley
v
25°
horizontal
Fig. 4.1
The slope makes an angle of 25° with the horizontal. A constant resistive force FR acts up the
slope on the trolley.
At time t = 0, the trolley has velocity v = 0.50 m s−1 down the slope.
At time t = 4.0 s, v = 12 m s−1 down the slope.
(a) (i)
Show that the acceleration of the trolley down the slope is approximately 3 m s−2.
[2]
(ii)
Calculate the distance x moved by the trolley down the slope from time t = 0 to t = 4.0 s.
x = ..................................................... m [2]
(iii)
On Fig. 4.2, sketch the variation with time t of distance x moved by the trolley.
x
0
0
4.0
t/s
Fig. 4.2
[2]
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(b) The mass of the trolley is 2.0 kg.
(i)
Show that the component of the weight of the trolley down the slope is 8.3 N.
[1]
(ii)
Calculate the resistive force FR.
FR = ...................................................... N [2]
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3
(a) Force is a vector quantity. State three other vector quantities.
1. ...............................................................................................................................................
2. ...............................................................................................................................................
3. ...............................................................................................................................................
[2]
(b) Three coplanar forces X, Y and Z act on an object, as shown in Fig. 3.1.
Y
object
θ
X
Z
Fig. 3.1
The force Z is vertical and X is horizontal. The force Y is at an angle θ to the horizontal. The
force Z is kept constant at 70 N.
In an experiment, the magnitude of force X is varied. The magnitude and direction of force Y
are adjusted so that the object remains in equilibrium.
Fig. 3.2 shows the variation of the magnitude of force Y with the magnitude of force X.
130
Y/N
110
90
70
50
0
20
40
60
80
100
120
X /N
Fig. 3.2
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(i)
Use Fig. 3.2 to estimate the magnitude of Y for X = 0.
Y = ...................................................... N [1]
(ii)
State and explain the value of θ for X = 0.
...........................................................................................................................................
...........................................................................................................................................
.......................................................................................................................................[2]
(iii)
The magnitude of X is increased to 160 N. Use resolution of forces to calculate the value
of
1.
angle θ,
θ = ........................................................ ° [2]
2.
the magnitude of force Y.
Y = ...................................................... N [2]
(c) The angle θ decreases as X increases. Explain why the object cannot be in equilibrium for
θ = 0.
...................................................................................................................................................
...................................................................................................................................................
...............................................................................................................................................[1]
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15
3
(a) State Newton’s first law of motion.
...................................................................................................................................................
.............................................................................................................................................. [1]
(b) A box slides down a slope, as shown in Fig. 3.1.
v
box
20°
horizontal
Fig. 3.1
The angle of the slope to the horizontal is 20°. The box has a mass of 65 kg. The total resistive
force R acting on the box is constant as it slides down the slope.
(i)
State the names and directions of the other two forces acting on the box.
1. ........................................................................................................................................
2. ........................................................................................................................................
[2]
(ii)
The variation with time t of the velocity v of the box as it moves down the slope is shown
in Fig. 3.2.
8.0
6.0
v / m s–1
4.0
2.0
0
0
1.0
Fig. 3.2
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t /s
2.0
16
1. Use data from Fig. 3.2 to show that the acceleration of the box is 2.6 m s–2.
[2]
2. Calculate the resultant force on the box.
resultant force = ...................................................... N [1]
3. Determine the resistive force R on the box.
R = ...................................................... N [3]
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