Question

8. A girl is travelling on her bike at a speed 2.54 m/s. If the
girl and her bike have a kinetic energy of 193 J, what is the combined mass of the girl and her bike? Show all
your work.

Answer 1

Given:-

• Velocity ,v = 2.54 m/s²

• Kinetic Energy ,KE = 193 J

To Find:-

• Combined mass of girl and bike ,m

Solution:-

As we know that the energy posses by body due to its motion is called Kinetic Energy.

• KE = 1/2mv²

Where,

KE is the Kinetic Energy

m is the mass

v is the velocity

Substitute the value we get

→ 193 = 1/2×m × 2.54²

→ 193 = 1/2×m × 6.45

→ 193×2 = m×6.45

→ 386 = m × 6.45

→ m = 386/6.45

→ m = 59.83 ≈ 60 kg

Therefore, the combined mass of the girl and her bike is 60 Kg.

Answer 2

Answer:

Given :-

• A girl is travelling on her bike at a speed of 2.54 m/s².
• The girl and her bike have a kinetic energy of 193 J.

To Find :-

• What is the combined mass of the girl and her bike.

Formula Used :-

$\boxed{\bold{\large{Kinetic\: Energy\: =\: \dfrac{1}{2} \times m{v}^{2}}}}$

where,

• m = Mass
• v = Velocity

Solution :-

Given :

• v = 2.54 m/s²
• K.E = 193 J

According to the question by using the formula we get,

⇒ 193 = $\dfrac{1}{2}$ × m × (2.54)²

⇒ 193 = $\dfrac{1}{2}$ × m × 6.45

⇒ 193 = $\dfrac{6.45}{2}$ × m

⇒ 386 = 6.45 × m

⇒ $\dfrac{386}{6.45}$ = m

⇒ 59.84 = m

➠ m = 59.84 kg ≈ 60 kg

$\therefore$ The combined mass of the girl and her bike is 60 kg .

✦ Extra Information ✦

❖ Kinetic Energy ❖

• Kinetic energy is the energy possessed by the body by virtue of its motion.
• Kinetic energy is a scaler quantity.
• The S.I unit of Kinetic energy is Joule which is equal to 1 kg.m².s²-².
• The C.G.S unit of Kinetic energy is erg.