The diagram shows a sailing boat travelling north across a lake. The force from the sail is 1.20 kN north. A water current produces a force of 0.350 kN sout...
Question 1 Report
The diagram shows a sailing boat travelling north across a lake. The force from the sail is 1.20 kN north. A water current produces a force of 0.350 kN south, and drag produces a force of 0.180 kN south. The mass of the boat, crew and equipment is 1.34 tonnes. It starts from rest.
(a) State what is meant by a vector quantity. [2]
(b) Complete the conversions.
1.34 tonnes = ........ kg
1.20 kN = ........ N [3]
(c) Calculate the resultant force on the boat. Give its direction. [3]
(d) Calculate the acceleration of the boat. [3]
(e) When this acceleration acts for 20 s, calculate the speed of the boat. [2]
(f) Describe how to draw a scale vector diagram to find the resultant force. [3]
(g) Explain why it would be incorrect to add all three force magnitudes without considering their directions. [2]
Answer Details
(a) A vector quantity has magnitude [1] and direction [1].
(b) \[1.34\ \mathrm{tonnes}=1340\ \mathrm{kg}\]
\[1.20\ \mathrm{kN}=1200\ \mathrm{N}\]
Conversions: \(1340\ \mathrm{kg}\) [1] and \(1200\ \mathrm{N}\) [2].
(c) The southward forces total:
\[350\ \mathrm{N}+180\ \mathrm{N}=530\ \mathrm{N}\]
\[F_\text{resultant}=1200\ \mathrm{N}-530\ \mathrm{N}=670\ \mathrm{N}\]
Resultant force = \(670\ \mathrm{N}\) north [3].
(d) \[a=\frac{F}{m}=\frac{670\ \mathrm{N}}{1340\ \mathrm{kg}}=0.50\ \mathrm{m\,s^{-2}}\]
Acceleration = \(0.50\ \mathrm{m\,s^{-2}}\) [3].
(e) The boat starts from rest, so \(u=0\):
\[v=u+at=0+(0.50\ \mathrm{m\,s^{-2}}\times20\ \mathrm{s})=10\ \mathrm{m\,s^{-1}}\]
Speed = \(10\ \mathrm{m\,s^{-1}}\) [2].
(f) Choose and state a suitable scale, such as \(1\ \mathrm{cm}=100\ \mathrm{N}\) [1]. Draw the three force arrows to scale in their correct directions, head-to-tail [1]. Measure the resultant arrow and convert its length using the scale [1].
(g) The forces act in opposite directions [1]. Therefore they must be combined as vectors, so opposing forces are subtracted rather than all magnitudes being added [1].
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