Answers
Question 1: Multiple Choice (2 marks each)
1.1 C 1.2 A 1.3 C 1.4 C 1.5 B 1.6 B 1.7 A 1.8 B 1.9 C 1.10 A
Question 2: Detailed Explanations and Calculations
Question 2.1: Define the term resultant vector. (2 marks)
A resultant vector is the vector that results from the combination of two or more vectors. It represents the cumulative effect of the individual vectors in both magnitude and direction, and is found by vector addition.
Question 2.2: Explain why Alfred is incorrect regarding the resultant force. (2 marks)
Alfred is incorrect because he is assuming that the forces he and Betty are applying are balanced. However, since both are applying force to lift the fridge, the combined upward force (the resultant force) must overcome the weight of the fridge. Therefore, the resultant force is not zero unless the weight of the fridge equals the sum of their upward forces.
Question 2.3: Calculate the vertical component of the force that Alfred applies (FA). (2 marks)
To find the vertical component of Alfred's force (\(F_A\)), we can use the formula:
\[ F_{Ay} = F_A \cdot \sin(\theta) \]
where \(F_A = 230 , N\) and \(\theta = 47^\circ\).
Calculating:
\[ F_{Ay} = 230 \cdot \sin(47^\circ) \approx 230 \cdot 0.7314 \approx 168.2 , N \]
Question 2.4: Calculate the horizontal component of the force that Alfred applies (FA). (2 marks)
To find the horizontal component of Alfred's force (\(F_{Ax}\)), we use the formula:
\[ F_{Ax} = F_A \cdot \cos(\theta) \]
Calculating:
\[ F_{Ax} = 230 \cdot \cos(47^\circ) \approx 230 \cdot 0.6810 \approx 156.6 , N \]
Question 2.5: Calculate the maximum weight of the fridge that Alfred and Betty are able to lift from the ground. (4 marks)
First, calculate the vertical component of Betty's force (\(F_B\)):
\[ F_{By} = F_B \cdot \sin(30^\circ) \]
where \(F_B = 200 , N\).
Calculating:
\[ F_{By} = 200 \cdot \sin(30^\circ) = 200 \cdot 0.5 = 100 , N \]
Now, combine the vertical components of both Alfred's and Betty's forces to find the maximum weight they can lift.
\[ F_{\text{total}} = F_{Ay} + F_{By} = 168.2 , N + 100 , N = 268.2 , N \]
Therefore, the maximum weight of the fridge that they are able to lift is approximately 268.2 N.
Question 2.6: Explain why Alfred and Betty were wrong for using two pulleys instead of just one. (2 marks)
Using two pulleys does not necessarily increase the lifting efficiency for this situation. One pulley would suffice to lift the fridge with the applied force. Adding another pulley may complicate the system without offering a mechanical advantage if both forces are directed upward at an angle. The combined effort could have been achieved with a single pulley, making the process more straightforward and potentially reducing the risk of tangling ropes. The force components would work more efficiently with just one system.