9702/Oct Nov/13/2013/Q16

The graph shows how the total resistive force acting on a train varies with its speed.

Part of this force is due to wheel friction, which is constant. The rest is due to wind resistance.

What is the ratio wind resistance/wheel friction at a speed of 200 km h^–1?

A 4
B 5
C 8
D 10

Solution:

Answer: A

The wheel friction is constant and the wind resistance increases with speed.

When the speed is zero, the wind resistance is also zero. So, wheel friction = 8 kN.

At a speed of 200 km h^–1, the total resistive force is 40 kN.

Wheel friction = 8 kN

Wind resistance = 40 – 8 = 32 kN

Ratio = wind resistance / wheel friction = 32 / 8 = 4

Reference: PYQ - Oct/Nov 2013 Paper 13 Q16

9702/May Jun/13/2015/Q16

The diagrams represent systems of coplanar forces acting at a point. The lengths of the force
vectors represent the magnitudes of the forces.

Which system of forces is in equilibrium?

Solution:

Answer: A.

For the forces to be in equilibrium, the resultant horizontal and vertical components of the force vectors should be zero.

The lengths of the vectors represent the magnitudes. Note that the diagonal vectors in the diagrams will have vertical and horizontal components less than the magnitude of the diagonal vector itself {this is obvious since the diagonal vector and its components form a right-angled triangle with the diagonal vector as the hypotenuse. The hypotenuse has the longest length in a right-angled triangle}.

Therefore, in these diagrams, the horizontal and vertical components of the diagonal vectors should be equal in length (and opposite in direction) as the horizontal and vertical vectors already given.

Diagram A:
The horizontal and vertical components of the diagonal vector are equal in magnitude and opposite in direction to the respective vectors already given. So, in diagram A, the system of forces is in equilibrium.

Diagram B:
The sum of the upward vertical components of the 2 diagonal vectors is greater than the downward vertical vector already present. So, the system of forces is not in equilibrium.

Diagram C:
The sum of the horizontal components (toward the left) of the 2 diagonal vectors is smaller than the horizontal vector (toward the right) already present. So, the system of forces is not in equilibrium.

Diagram D:
The system is not balanced vertically since the downward vertical component of one of the diagonal vectors is greater than the upward vertical component of the other diagonal vector.

Reference: PYQ - May/Jun 2015 Paper 13 Q16

9702/Oct Nov/13/2016/Q16

An air-conditioning unit is supported by a rigid beam PQ, as shown.

 Which diagram shows the directions of the horizontal and vertical forces acting on the ends of the
beam?

Solution:

Answer: B.

The resultant force is the tension which is point to opposite direction as shown in figure below.
Follow the vector concept, only choice B is make sense and fulfill the condition.

Since the air-conditioning unit is in equilibrium, the resultant force on the system is zero.

The weight of the unit acts on the beam PQ. Since the beam is inclined the force appears along the beam, from P to Q.

Breaking down this force results in a component to the right and a component downwards.

Now, end Q of the beam is in contact with the wall. From Newton’s 3^rd law, the wall would also exert a (contact) force on the beam at Q. This force is from Q to P (opposite in direction of the initial force).

Resolving this force gives a component upwards and a component to the left.

We can still observe that the overall force on the system is zero.

Reference: PYQ - Oct/Nov 2016 Paper 13 Q16