IEMDaily - Video Lecture Notes

Example

Readings of Weighing Machine in Accelerated frames

A man stands on a weighing machine kept inside a lift. Initially the lift is ascending with the acceleration 'a' due to which the reading is

N

. Now the lift descends with the same acceleration and reading is 10% of initial. The acceleration of the lift is given by:

N = m (g + a)

N^{'} = m (g - a)

N^{'} = \frac{10}{100} \times N

m (g - a) = \frac{m (g + a)}{10}

10 g - 10 a = g + a

9 g = 11 a \Rightarrow

a = \frac{9 g}{11}

Definition

Motion of Blocks on Moving Wedges

A particle B of mass

0.6

kg slides down the smooth face PR of a wedge A of mass

1.7

kg which can move freely on a smooth horizontal surface. If the inclination of the face PR to the horizontal is

45^{o}

, then motion parameters can be estimated in the following way:

Let acceleration of the wedge A is

a

N + m a s i n θ = m g c o s θ

N s i n θ = M a

M a = (m g c o s θ - m a s i n θ) s i n θ

a (M + m s i n^{2} θ) = m g c o s θ s i n θ

The acceleration of wedge A is

a = \frac{m g s i n θ c o s θ}{M + m s i n^{2} θ}

Now we know ,

(θ = 45^{0})

= \frac{(0.6) g s i n 45^{0} c o s 45^{0}}{1.7 + (0.6) s i n^{2} 45^{0}}

= \frac{3 g}{20}

Acceleration of

m

relative to the wedge

= a c o s θ + g s i n θ

Vertical component

= (a c o s θ + g s i n θ) s i n θ

= (\frac{3 g}{20} + g) \frac{1}{2}

= \frac{23 g}{40}

\Rightarrow

Horizontal component

=

(Vertical component)

- a

= \frac{23 g}{40} - \frac{3 g}{20}

= \frac{17 g}{40}

Definition

Condition of total equilibrium

A body is considered to be in total equilibrium if net force and net torque acting on it zero.
For equilibrium:

F_{n e t} = 0

τ_{n e t} = 0

Definition

Vector analysis on concurrent forces

If the forces applied to a body are such that their lines of action meet at a single point, then they are called concurrent forces. Resultant of multiple forces on a body can be found using triangle and parallelogram law of vector addition and simplifies the problem solving by finding the net force on the particle.

Example:
An object is in equilibrium under four concurrent forces in the directions shown in figure. Find the magnitude of