Question 28
(a)
State the two conditions for a system to be in equilibrium. [2]
(b)
A paraglider P of mass 95 kg is pulled by a wire attached to a boat,
as shown in Fig. 2.1.
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.
Fig.
2.2
(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. [2]
(iii)
Calculate the change in kinetic energy of P from time t
= 0 to t = 7.0 s. [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, [3]
2.
the force R due to air resistance
acting on P in the horizontal direction. [3]
[Total: 14]
Reference: Past Exam Paper – June 2017 Paper 21 Q2
Solution:
(a)
resultant force (in any direction) is zero
resultant torque/moment (about any point) is
zero
(b)
(i)
{We
can either use the formula a = v-u / t or the gradient of the graph. The graph
at t = 5.0 s is a straight line, so the gradient is constant.}
a = (v − u) / t or gradient or Δv / (Δ)t
{Example: consider the points (7.0, 8.8) and
(4.0, 4.6)}
e.g. a = (8.8 − 4.6) / (7.0 – 4.0) = 1.4 m s-2
(ii)
{The
distance travelled is given by the area under the velocity-time graph. The area
may be broken down into a rectangle and a trapezium.
Area
of rectangle (from t = 0 to t = 4.0 s) = (4.6 × 4) m
Area
of trapezium (from t = 4.0 s to t = 7.0 s) = ½ × (8.8
+ 4.6) × 3 m
Recall: area of trapezium = ½ × sum of parallel sides × height}
s = (4.6×4) + [(8.8 + 4.6) / 2] × 3
s = 18.4 + 20.1
s = 39 (38.5) m
(iii)
{KE = ½ mv2
We need to consider the
speeds at t = 0 s and at t = 7.0 s.}
ΔE = ½ × 95 × [(8.8)2 − (4.6)2]
ΔE = 3678 – 1005
ΔE = 2700 (2673) J
(iv)
1.
{Since the boat is moving horizontally, the resultant
vertical force is zero at P.
Forces at P: Weight (down), Vertical component
of tension (down), Lift force F (up)
Lift F = Vertical component of tension + Weight
W = mg}
weight = 95 × 9.81 (= 932 N)
vertical tension force = 280 sin 25° or 280 cos 65° (=118.3 N)
{Lift F = Vertical component
of tension + Weight}
F = 932 + 118
F = 1100 (1050) N
2.
{Resultant force = Horizontal tension force –
Air resistance R}
horizontal tension force = 280 cos 25° or 280 sin 65° (= 253.8 N)
{Resultant force = ma}
resultant force = 95 × 1.4 (= 133 N)
133 = 253.8 – R
R = 120 (120.8) N
In biv part 1. how do we figure out the arrow on the resultant tension force (wire) is towards the boat and not towards the paraglider?
ReplyDeleteI took it towards the paraglider and hence got the vertical component of the tension force upwards.
it is accelerating, so the resultant force should be forwards, towards the boat
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