Question

A loaded lorry of mass 1200 kg moves with a velocity 12 m/s. its velocity become

10 m/s after 5 s.

a)what is the change in momentum?​
b)what is the rate of change of momentum?

Answer 1

Answer :

• Change in momentum or impulse of the lorry is 2400 Kg m/s.
• Rate of change of momentum or force of the lorry is 480 N

Explanation :

Given :

• Mass of the lorry, m = 1200 kg
• Initial velocity of the lorry, u = 12 m/s
• Final velocity of the lorry, v = 10 m/s

To find :

• Change in momentum, ∆p = ?
• Rate of change of momentum, F = ?

Knowlwdge required :

Change in momentum of a object is equal to the Impulse experienced by the object.

So,

⠀⠀⠀⠀⠀⠀⠀⠀⠀∆p = m(v - u)

Where,

• ∆p = Change in momentum
• m = Mass of the body
• v = Final velocity of the body
• u = Initial velocity of the body

Rate of change in momentum of the body is equal to the force exerted by the body.

So,

⠀⠀⠀⠀⠀⠀⠀⠀⠀P = ma

Where,

• P = Rate of change of momentum
• m = Mass of the body
• a = Acceleration produced by the bod

First equation of motion :

⠀⠀⠀⠀⠀⠀⠀⠀⠀v = u + at

Where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time Taken

Solution :

To find the change in momentum :

By using the formula for change in momentum and substituting the values in it, we get :

⠀⠀=> ∆p = m(v - u)

⠀⠀=> ∆p = 1200 × (10 - 12)

⠀⠀=> ∆p = 1200 × (-2)

⠀⠀=> ∆p = -2400

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ ∆p = -2400 kg m/s

Let's find out the acceleration produced by the lorry :

By using the first equation of motion and substituting the values in it, we get :

⠀⠀=> v = u + at

⠀⠀=> 10 = 12 + a(5)

⠀⠀=> 10 - 12 = 5a

⠀⠀=> -2 = 5a

⠀⠀=> -2/5 = a

⠀⠀=> -0.4 = a

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ a = -0.4 m/s²

Hence the accelaration of the lorry is -0.4 m/s².

To find the rate of change in momentum :

By using the formula for rate of change in momentum and substituting the values in it, we get :

⠀⠀=> P = ma

⠀⠀=> P = 1200 × (-0.4)

⠀⠀=> P = -480

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ p = -480 N

Therefore,

• Change in momentum, ∆p = -2400 kg m/s
• Rate of change of momentum, F = -480 N

Answer 2

Answer:

$\huge \bf \: Answer(1)$

• Mass of lorry (M) = 1200 kg
• Initial velocity (U) = 12 m/s
• Final velocity (V) = 10 m/s

Now,

As we know that

$\huge \bf \triangle p = m(v - u)$

$\tt \implies \triangle p = 1200(10 - 12)$

$\tt \implies \triangle p \: = 1200( - 2)$

$\huge \boxed { \tt \triangle p \: = -2400 }$

Here,

∆P = Change in mounmentum

M = Mass

V = Final velocity

U = Initial velocity

$\huge \bf \: Answer \: (2)$

For this first we have to find acceleration of body.

$\sf \implies \: v \: = u + at$

Here,

V = Final velocity

U = Initial velocity

A = Acceleration

T = Time

$\sf \implies \: 10 = 12 + a(5)$

$\sf \implies \: 10 - 12 = 5a$

$\sf \implies \: - 2 = 5a$

$\sf \implies \: a \: = \dfrac{ -2}{ 5}$

$\huge \boxed { \bf \: a \: = -0.4 \: {m \: per \: s}^{2} }$

Now,

Finding rate of change of momentum

$\huge \bf \: P \: = ma$

$\sf \implies \: p = 1200 \times ( - 0.4)$

$\sf \implies - 480$

$\huge \fbox {p \: = -480 N}$