Question

An object of mass 100kg is accelerated uniformly from a velocity of 5m/s to 8m/s in 6s.
Calculatetheinitialandfinalmomentum ofthe object.Also,findthemagnitude oftheforce
exerted on the object

Answer 1

GIVEN:

• Mass of the object, m = 100 kg
• Initial velocity, u = 5 m/s
• Final velocity, v = 8 m/s
• Time, t = 6 sec

TO FIND:

• Initial momentum , p
• Final momentum , P
• Force exerted on the object, f

FORMULAE:

• According to first equation of motion, v = u + at

• According to Newton's second law of motion, f = ma

• Momentum, p = mv

SOLUTION:

STEP 1: TO FIND INITIAL MOMENTUM:

$p = mu \\ \\ p = 100 \times 5 \\ \\ p = 500 \: kgm/s$

Initial momentum is 500 kgm/s

STEP 2: TO FIND FINAL MOMENTUM:

$P = mv \\ \\ P = 100 \times 8 \\ \\ P = 800 \: kgm/s$

Final momentum is 800 kgm/s

STEP 3: TO FIND ACCELERATION:

$v = u + at \\ \\ 8 = 5 + 6a \\ \\ 6a = 8 - 5 \\ \\ 6a = 3 \\ \\ a = \frac{3}{6} \\ \\ a = \frac{1}{2} \\ \\ a = 0.5 \: \dfrac{m}{ {s}^{2} }$

Acceleration of the object is 0.5 m/s²

STEP 4: TO FIND FORCE:

$f = ma \\ \\ f = 100 \times 0.5 \\ \\ f = 50 \: newton$

Force exerted on the object is 50 N

ANSWER:

• Initial momentum is 500 kgm/s
• Final momentum is 800 kgm/s
• Force exerted on the object is 50 N

NOTE:

Force can be found by another method.

According to Newton's second law of motion, force is equal to rate of change of momentum.

f = dp/dt

f = (800 - 500) / 6

f = 300 / 6

f = 50 N

Answer 2

Answer:

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Explanation:

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GIVEN:

Mass of the object, m = 100 kg

Initial velocity, u = 5 m/s

Final velocity, v = 8 m/s

Time, t = 6 sec

TO FIND:

Initial momentum , p

Final momentum , P

Force exerted on the object, f

FORMULAE:

According to first equation of motion, v = u + at

According to Newton's second law of motion, f = ma

Momentum, p = mv

SOLUTION:

STEP 1: TO FIND INITIAL MOMENTUM:

Initial momentum is 500 kgm/s

STEP 2: TO FIND FINAL MOMENTUM:

Final momentum is 800 kgm/s

STEP 3: TO FIND ACCELERATION:

Acceleration of the object is 0.5 m/s²

STEP 4: TO FIND FORCE:

Force exerted on the object is 50 N

ANSWER:

Initial momentum is 500 kgm/s

Final momentum is 800 kgm/s

Force exerted on the object is 50 N

NOTE:

Force can be found by another method.

According to Newton's second law of motion, force is equal to rate of change of momentum.

f = dp/dt

f = (800 - 500) / 6

f = 300 / 6

f = 50 N