Question

An object of mass 100 kg is accelerated uniformly from a velocity of 5 ms–1 to 8 ms–1 in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.

Answer 1

Answer :-

Initial momentum = 500kg m/s

Final momentum = 800kg m/s

Force = 50N

Explanation :-

Given :

Mass of the object,m = 100kg

Initial velocity,u = 5/m

Final velocity,v = 8m/s

To Find :

Initial momentum = ?

Final momentum = ?

Force => ?

Solution :

We know,

$\sf{}p=mv$

Here,

p is the momentum,

m is the mass and,

v is the velocity.

So,

Initial momentum,

$\sf{}\implies 100kg\times 5m/s$

$\sf{}\therefore 500kg\ m/s$

Therefore,initial momentum is equal to 500kg m/s

Final momentum,

$\sf{}\implies 100kg\times 8m/s$

$\sf{}\therefore 800kg\ m/s$

Therefore,final momentum is equal to 800kg m/s

We know,

$\sf{}F=ma$

here,

F is the force applied,

m is the mass and,

a is the acceleration.

We don’t know acceleration,so let’s find out the accentuation first.

According to the first equation of motion

$\sf{}v=u+at$

$\sf{}:\implies 8=5+a\times 6$

$\sf{}:\implies 8-5=a\times 6$

$\sf{}:\implies 3=a\times 6$

$\sf{}:\implies \dfrac{3}{6}=a$

$\sf{}\therefore a=0.5m/s^2$

Put their values and solve it.

$\sf{}:\implies 100\times 0.5$

$\sf{}\therefore 50N$

Therefore,force is equal to 50N

Answer 2

Answer:

• Initial momentum = 500 kg.ms-¹
• Final momentum = 800 kg.ms-¹
• Force = 50 N

Explanation:

Given that,

• Mass (m) = 100kg
• Initial velocity (u) = 5 ms-¹
• Final velocity (v) = 8 ms-¹
• Time (t) = 6 sec

As we know that,

Momentum = mass × Velocity.

[ For initial ]

▶p1 = m × u

▶p1 = 100 × 5

▶p1 = 500 kg. ms-¹

[ For Final ]

▶p2 = m × v

▶p2 = 100 × 8

▶p2 = 800 kg. ms-¹

Applying acceleration formula,

▶ a = (v - u)/t

▶a = (8 - 5)/6

▶a = 3/6

▶a = 0.5 m/s²

Now, we know that,

▶F = ma

▶F = 100 × 0.5

▶F = 50 N

Hence,

• The magnitude of the force exerted on the object is 50 N.