Question

46. Two forces 10 N each inclined to each
other at angle 120° act on a 6 kg mass at
rest.Its kinetic energy after 12 s is
2) 1200 J
3) 600 J
4) 900 J
1) 400 J



Hey guys pleaseee solve this question asap i have an exam tomorrow! Thankyou! And appropriate answers only pls

Answer 1

Answer:

• Kinetic energy = 1200 J

Explanation:

Given:

Two forces of 10 N are inclined to each other at an angle of 120°.

• So, Let two forces, A = B = 10 N
• The angle between the forces be, x = 120°

Also,

• Mass of body, m = 6 kg

We need to find:

• The kinetic energy of particle after time 't = 12 s', K.E. =?

Formula required:

• Formula to calculate the Resultant 'F' of two vectors (forces) 'A' and 'B' which are inclined at an angle 'x' with each other.

         F^2 = A^2 + B^2 + 2 AB cos x

• The Expression for Newton's second law of motion

         F = m a

• First equation of motion

         v = u + a t

• Formula to calculate kinetic energy

         KE = 1/2 m v^2

[ Where F is force, m is mass, a is acceleration, u is initial velocity, v is final velocity, t is the time taken and KE is the kinetic energy of the body.]

Solution:

Calculating the resultant force acting on the particle.

Using formula

→ F^2 = A^2 + B^2 + 2 AB cos x

→ F^2 = 10^2 + 10^2 + 2 · 10 · 10  cos 120°

→ F^2 = 200 - 100

→ F = 10 N

Now, Using Newton's second law of motion calculating the acceleration produced ( a=? )

→ F = m a

→ 10 = 6 · a

→ a = 10/6

→ a = 5/3  m/s^2

Further, Using the first equation of motion to calculate the velocity (v=?) of the particle on applying force.

→ v = u + a t

[ Taking u = 0 since, initially particles was at rest ]

→ v = 0 + 5/3 · 12

→ v = 20 m/s

At last, Using the formula to calculate Kinetic energy (K.E. =?) of particle

→ K.E. = 1/2 m v^2

→ K.E. = 1/2 · 6 · 20^2

→ K.E. = 3 · 400

→ K.E. = 1200 J

Therefore,

• Kinetic energy would be 1200 Joules.

Answer 2

Answer:

✯ Given :-

• Two forces 10 N each inclined to each other at an angle of 120° act on a 6 kg mass at rest .

✯ To Find :-

• Kinetic energy after 12 seconds is ?

✯ Solution :-

⋆ Given :-

• F₁ = F₂ = 10 N
• Q = 120°
• mass = 6 kg
• time = 12 sec

» So, the resultant force is Fnet = 10 N

⇨This force acts midway between the direction of two forces,

◩ Hence, the acceleration of a body,

➙ a = $\dfrac{10}{6}$ = $\dfrac{5}{3}$ m/s²

◪ So, the velocity after t = 12 secs is,

➙ v = at ⇒ $\dfrac{5}{3}$ × 12 ⇒ 20 m/s

◪ $\mapsto$ The kinetic energy (K.E) is,

➙ K.E = $\dfrac{1}{2}$mv²

⇒ K.E = $\dfrac{1}{2}$ × 6 × (20)²

⇒ K.E = 3 × 400

➥ K.E = 1200 J

$\therefore$ Kinetic energy after 12 seconds will be $\boxed{\bold{\small{1200\: J}}}$ .

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