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Thursday, July 25, 2019

A paraglider P of mass 95 kg is pulled by a wire attached to a boat, as shown in Fig. 2.1.


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

2 comments:

  1. 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?

    I took it towards the paraglider and hence got the vertical component of the tension force upwards.

    ReplyDelete
    Replies
    1. it is accelerating, so the resultant force should be forwards, towards the boat

      Delete

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