Question 1
1
A sphere of radius 2.1 mm falls with terminal (constant) velocity through a liquid, as shown in Fig. 1.1. Three forces act on the moving sphere. The weight of the sphere is \(7.2 \times 10^{-4} \mathrm{~N}\) and the upthrust acting on it is \(4.8 \times 10^{-4} \mathrm{~N}\). The viscous force \(F_{\mathrm{V}}\) acting on the sphere is given by where r is the radius of the sphere, v is its velocity and k is a constant. The value of k in SI units is 17 .
structured8 marks
Question 1(c)
1(c)
8 marks
Question 1(c)(ii)
1(c)(ii)
Determine the magnitude of the terminal (constant) velocity of the sphere.
Mediumstructured8 marks
Answer
\[ \begin{aligned} F_{\mathrm{V}} =7.2 \times 10^{-4}-4.8 \times 10^{-4} =2.4 \times 10^{-4}(\mathrm{~N}) \end{aligned} \] C1 \[ \begin{aligned} \text { velocity } =2.4 \times 10^{-4} /\left(17 \times 2.1 \times 10^{-3}\right) =6.7 \times 10^{-3} \mathrm{~m} \mathrm{~s}^{-1} \end{aligned} \] A1 Question Marks
Question 2
2
A sphere floats in equilibrium on the surface of sea water of density \(1050 \mathrm{~kg} \mathrm{~m}^{-3}\), as shown in Fig. 2.1.
structured8 marks
Question 2(b)
2(b)
The sphere is now held so that its entire volume is below the surface of the water. The sphere is then released.
structured3 marks
Question 2(b)(ii)
2(b)(ii)
The sphere accelerates upwards but remains entirely below the surface of the water. State and explain what happens to the acceleration of the sphere as its velocity begins to increase.
Mediumstructured3 marks
Answer
the (downward) drag / viscous force increases (with speed) M1 resultant force decreases (as upthrust and weight remain the same) M1 acceleration decreases (as its velocity increases) A1
Question 2
2
A ball is thrown from a point P , which is at ground level, as illustrated in Fig. 2.1. The initial velocity of the ball is \(12.4 \mathrm{~m} \mathrm{~s}^{-1}\) at an angle of \(36^{\circ}\) to the horizontal. The ball just passes over a wall of height h. The ball reaches the wall 0.17 s after it has been thrown.
structured2 marks
Question 2(b)
2(b)
A second ball is thrown from point P with the same velocity as the ball in (a). For this ball, air resistance is not negligible. This ball hits the wall and rebounds. On Fig. 2.1, sketch the path of this ball between point P and the point where it first hits the ground.
Mediumstructured2 marks
Answer
smooth curve with ball hitting wall below original B1 smooth curve showing rebound to ground with correct reflection at wall B1
Question 2
2
A ball is thrown horizontally from the top of a building, as shown in Fig. 2.1. The ball is thrown with a horizontal speed of \(8.2 \mathrm{~ms}^{-1}\). The side of the building is vertical. At point P on the path of the ball, the ball is distance x from the building and is moving at an angle of \(60^{\circ}\) to the horizontal. Air resistance is negligible.
structured2 marks
Question 2(b)
2(b)
The path of the ball in (a), with an initial horizontal speed of \(8.2 \mathrm{~m} \mathrm{~s}^{-1}\), is shown again in Fig. 2.2. On Fig. 2.2, sketch the new path of the ball for the ball having an initial horizontal speed
structured2 marks
Question 2(b)(ii)
2(b)(ii)
equal to \(8.2 \mathrm{~m} \mathrm{~s}^{-1}\) but with air resistance (label this path A ).
Mediumstructured2 marks
Answer
smooth path curved and below given path hits ground at steeper angle