4.1 Scalars & Vectors

A gymnast of mass 65 kg is holding himself stationary on the rings.

The angle between the gymnast’s arms and the ropes is 68 ^o.

What is the tension, T, in each rope?

A punching bag is suspended from a light, in extensible rope, and is pushed with a force of 300 N to the left, making a stationary angle between the supporting rope and the vertical of 23^o.

Calculate the mass of the bag.

A uniform rectangular block sits on a rough slope inclined at 36 ^o to the horizontal. The block is at rest and the static friction is 41 N as shown. 

When the mass of the block is increased by 23% the block begins to accelerate down the slope.

What is the new mass of the block?

A barge travels straight along a canal at a steady speed. A horse is towing the barge, and a person walks on the other bank holding a rope under a tension of 20 N.

The drag experienced by the barge is 50 N.

Which line, A to D, in the table below correctly gives the magnitude of the tension caused by the towing horse and the angle which the horse’s rope makes to the direction of motion?

The speed of a walker is denoted by v m s^–1. When walking up a hill inclined at angle  θ° to the horizontal, the walker travels a distance of s m. The walker travels for a time of t s.

Which of the following is not a correct expression for the height, h, obtained by the walker over their journey?

A uniform object of mass, m, sits at rest on a slope inclined at  θ° to the horizontal.

The magnitude of friction is given by F = μR where R is the normal reaction force and μ is a constant called the coefficient of friction.

Which of the following is not a possible expression for μ?

Three newtonmeters are attached to a board in fixed positions using nails. Strings are attached to each newtonmeter under tension at point P. One of the strings is horizontal.

The values on two of the newtonmeters are shown in the diagram below.

Which line, A to D, in the table below, gives the magnitude of force F on the third newtonmeter and the angle, θ , between F and the horizontal?

The force experienced by two charged particles can be given by Coulomb’s Law

F = 

Where F is the electrostatic force between them, q₁ and q₂ is the charge of each particle, r is the radial distance between them, and  is a constant with a value of 8.85 × 10^–12 F m^–1.

Two identically charged conducting spheres of mass 4.5 × 10^–3 kg are suspended in equilibrium by a non-conducting thread in the arrangement shown in the diagram.

The distance, r, between the centre of each sphere is 0.25 m. The charge on each sphere is 68 nC.

What is the tension, T, in one of the threads?

A uniform object of mass, m₁, sits at rest on a slope inclined at 45 ^o to the horizontal. The object is held in place by the tension in a rope which passes over a frictionless pulley and is attached to a free-hanging mass, m₂.

The mass of m₂ is 1kg. The mass of m₁ is unknown.

If the angle of the slope is increased to 60 ^o then m₁ will begin to slide down the slope. When the angle of the slope is decreased to 30 ^o then m₁ will start to move up the slope.

The magnitude of friction F is given by F = μR where R is the normal reaction force and μ is a constant called the coefficient of friction.

Which line, A to D, in the table below, gives the value of m₁ and the value of μ?

The speed of an aeroplane in still air is 200 km h^–1. The wind blows from the west at a speed of 85.0 km h^–1.

In which direction must the pilot steer the aeroplane in order to fly due north?

Vectors P and Q are drawn to scale.

Which diagram represents the vector (P – Q)?

A vector has magnitude R and perpendicular components P and Q, as shown in the diagram.

Which row correctly describes the perpendicular components?

The table shows the x-component and y-component of four force vectors.

Which force vector has the largest magnitude?

Coplanar forces of 13 N, 12 N and 5 N act on an object. Which force, in N, could not possibly be the resultant of these forces?

Square objects A, B, C and D are each acted on by three forces.

Which one of the objects is in equilibrium?

A block has a weight of 14 N and sits on a ramp inclined at 27^o to the horizontal.

What is the component of weight which is acting down the ramp?

A pendulum is oscillating from a fixed point. The bob at the end has weight 2.0 N.

At a given instant the angle of the string is inclined at 23 ^o to the vertical.

What is the component of weight which is parallel to the string?

Two forces act on a block. There is a downwards force of 45 N and a horizontal force of 27 N to the right.

Which line, A to D, in the table below correctly gives the magnitude resultant force and the angle it makes to the horizontal?