• Physics 9702 Doubts | Help Page 195

Question 944: [Kinematics > Air resistance]

A football is dropped from top of a tall building.

Which acceleration-time graph best represents motion of the football through the air?

Reference: Past Exam Paper – June 2008 Paper 1 Q8

Solution 944:

Answer: C.

Since the motion of the air is through the air, we should account for the effect of air resistance.

First of all, an acceleration-time graph is given. So, we need to consider the resultant acceleration of the football during its motion.

The acceleration of free fall, g causes a downward acceleration on the ball (due to its weight) and this is a constant value. Then, as the ball falls, air resistance acts on it due to its motion. Air resistance opposes motion and thus, acts upwards since ball is falling. This causes the resultant force, and thus the resultant acceleration of the ball to decrease with time. [C is correct]

Now, air resistance depends on the speed of the ball. (Even though acceleration decreases, the speed increases until the acceleration is zero – remember that acceleration is the rate of change of velocity, so as long as the acceleration is not zero, the speed will be changing.) As the speed of the ball increases, the air resistance becomes greater, until it is equal to the downward weight of the ball.Thus, the decrease in acceleration is not linear.

From this point, the resultant acceleration of the ball is zero – the ball is said to have reached its terminal speed. Since speed is no longer changing, air resistance is also constant and equal to magnitude to the weight.

Question 945: [Dynamics > Collisions]

Which statement about a ball that strikes a tennis racket and rebounds is always correct?

A Total kinetic energy of the ball is conserved.

B Total kinetic energy of the system is conserved.

C Total momentum of the ball is conserved.

D Total momentum of the system is conserved.

Reference: Past Exam Paper – November 2009 Paper 11 Q8 & Paper 12 Q7

Solution 945:

Answer: D.

For an elastic collision, both the total kinetic energy and total momentum of the system are conserved.

For an inelastic collision, the total kinetic energy of the system is not conserved but the total momentum of the system are conserved.

Thus, for any collision, the total momentum of the system is conserved. Not that the system consists of the ball and the tennis racket. Even if the velocity of one of them changes, the change in velocity of the other would account for the conservation of the momentum in the while system.

Question 946: [Matter > Changes of States]

Which row correctly states the characteristics of the process of evaporation?

Reference: Past Exam Paper – June 2013 Paper 11 Q20

Solution 946:

Answer: B.

For a substance to change from the liquid state to the gaseous state (for both evaporation and boiling), it requires energy. [C and D are incorrect]

Evaporation can occur at any temperature, while boiling occurs only at a particular temperature called the boiling point of the substance. [A is incorrect]

As boiling occurs, the substance loses some of its molecules that had energy greater than the average energy of the other molecules of the substance (this is why those molecules could escape through evaporation). Thus, the average kinetic energy of the molecules of the whole of the substance is now lower. This is represented as a decrease in temperature.

Question 947: [Kinematics > Projectile motion]

A projectile is launched at point O and follows path OPQRS, as shown. Air resistance may be neglected.

Which statement is true for the projectile when it is at the highest point Q of its path?

A The horizontal component of the projectile’s acceleration is zero.

B The horizontal component of the projectile’s velocity is zero.

C The kinetic energy of the projectile is zero.

D The momentum of the projectile is zero.

Reference: Past Exam Paper – November 2002 Paper 1 Q8 & June 2005 Paper 1 Q9 & June 2012 Paper 12 Q10

Solution 947:

Answer: A.

Since the acceleration due to gravity is vertically downward, at the highest point Q, where the direction of motion is to the right (horizontal velocity remains constant since air resistance, which opposes motion, is negligible [also, it is not affected by the vertically down acceleration], so the horizontal component of acceleration is zero).

At the highest point Q, there is no vertical upward component since the projectile has reached its maximum vertical height – it cannot go any higher.

The horizontal component of the projectile’s velocity is not zero since the motion continues towards the right (note that zero acceleration does not mean a speed of zero – it just means that the speed is not changing). [B is incorrect]

Both the kinetic energy and momentum of the projectile depends on its speed. Since the speed is not zero, the kinetic energy and momentum cannot be zero. [C and D are incorrect]

Question 948: [Gravitation]

The radius of the orbit of a plant X round the sun is 4 times the orbital radius of Earth. If a year on the planet is assumed to be the period of its revolution round the sun, what is the equivalent age of an eighty year old man in terms of the year on the planet X?

A 10                B 20                C 80                D 320              E 640

Reference: Pacific Physics A-Level, Volume 1 by POH LIONG YONG – Self Evaluation Exercise 9.2 Q7

Solution 948:

Answer: A.

To answer this question, we need to use Kepler’s 3^rd law of Gravitation which gives the relationship between the period and the radius of orbit of a planet. The law is derived below.

Suppose that a planet of mass m is in a circular orbit of radius r around the sun.

The centripetal force F is provided by the gravitational attraction on the planet by the sun.

F = GMm / r²               where M is the mass of sun

Therefore, GMm / r² = mrω²

GMm / r² = mr (2π / T)²           where T = period

T² / r³ = 4π² / GM = constant              (4π² / GM has a constant value)

T² / r³ = constant

T² ∝ r³

This relationship is known as Kepler’s 3^rd law of Gravitation.

Let the radius of the orbit of earth round the sun be R_E.

Radius of planet X round the sun = 4R_E

Let the period of revolution of earth round the sun to be T_E and that of planet X to be T_X.

From Kepler’s 3^rd law of gravitation,

T² ∝ r³

T² / r³ = constant

For Earth, T_E² / R_E³ = constant

For planet X, T_X² / (4R_E)³ = constant

Since both are orbiting round the sun, the ‘constant’ is the same in both cases.

T_X² / (4R_E)³ = T_E² / R_E³

T_X² = 64R_E³ × (T_E² / R_E³) = 64T_E²  

Period of revolution of planet X, T_X = 8T_E

That is, 1 year on planet X is equivalent to 8 years on earth. Thus, an 80-year old man on earth would have an equivalent age of 80 / 8 = 10 years on planet X.