Question

An object of Mass loo kg is accelerated<br />Uniformly at a velocity of 5 ms-1 to 8 ms-1<br />in 6s. calculate initial and final<br />momentum also find the magnitude<br />of the force exerted on the object.​

Answer 1

Answer:

• Initial Momentum = 500 kgm/s
• Final momentum = 800kgm/s
• Magnitude of Force = 50 Newton.

Explanation:

Given:-

• Mass ,m = 100 Kg
• Initial velocity ,u = 5m/s
• Final velocity ,v = 8m/s
• Time taken ,t = 6 s

To Find:-

• Initial Momentum ,pi
• Final momentum ,pf
• Force ,F

Solution:-

As we know that momentum is defined as the product of mass and velocity.

•p = mv

Where,

• p denote momentum
• m denote mass
• v denote velocity

Firstly we calculate the initial momentum .

• pi = mu

Substitute the value we get

→ pi = 100×5

→ pi = 500 kgm/s

• Hence, initial momentum of the body is 500 kgm/s.

Now , calculating the final momentum

• pf = mv

Substitute the value we get

→ pf = 100×8

→ pf = 800 kgm/s

• Hence, the final momentum of the body is 800 kgm/s.

Now , calculating the force .

Firstly we calculate the acceleration of the body.

• a = v-u/t

Substitute the value we get

→ a = 8-5/6

→ a = 3/6

→ a = 1/2 = 0.5 m/s²

Now, calculating the force

• F = ma

where,

• F is the force
• m is the mass
• a is the acceleration

Substitute the value we get

→ F = 100×0.5

→ F = 10×5

→ F = 50 N

• Hence, the Magnitude of Force is 50 Newton.

Answer 2

Answer:

Given :-

• Mass of object = 100 kg
• Initial velocity = 5 m/s
• Final velocity = 8 m/s
• Time taken = 6 sec

To Find :-

• Momentum
• Magnitude
• Force exerted

Solution :-

As we know that

$\huge \tt \: P = mv$

Here,

P denotes Momentum

M denotes Mass

V denotes Velocity

Firstly let's calculate initial Mounmentum

$\huge \fbox{PI = mu}$

Here,

PI = Initial Momentum

M = Mass

U = Initial Mounmentum

$\tt \: PI = 100 \times 5$

$\tt \: PI = 500 \: kg m/s$

Now,

Let's find final Mounmentum

As we know that

$\huge \fbox{PF = mv}$

Here,

PF = Final Momentum

M = Mass

V = Final Momentum

$\tt \: PF = 100 \times 8$

$\tt \: PF = 800 \: kg m/s$

Now,

Let's find Acceleration

$\huge \boxed{ \bf \: A = \dfrac{v - u}{t}}$

Here,

A = Acceleration

V = Final Momentum

U = Initial Momentum

T = Time

$\tt \: A = \dfrac{8 - 5}{6}$

$\tt \: A = \dfrac{3}{6}$

$\tt \: A = \dfrac{1}{2} \: = 0.5 \: mps$

Now,

Let's find force exerted

$\huge \fbox{F = ma}$

Here,

F = Force

M = Mass

A = Acceleration

$\tt \: F = 100 \times 0.5$

$\tt \: F = 50 \: N$