A 2.00-g lead bullet is shot into a wooden wall.As a result,the temperature of the bullet increases by 212 $\circ$ C.Assuming that all of its kinetic energy is absorbed as heat by the bullet,what was the speed of the bullet just prior to striking the wall?

Question

Quizplus · Accepted Answer

First, we need to convert the temperature change from Fahrenheit to Celsius:
ΔT=212°F=100°C

The increase in temperature of the bullet is equal to the change in its internal energy:
ΔU=mCΔT

where m is the mass of the bullet, C is its specific heat, and ΔT is the temperature change.

Assuming no heat is transferred to the surroundings, all of the kinetic energy of the bullet is converted to internal energy. Therefore, the initial kinetic energy of the bullet can be calculated as:

KE = (1/2)mv²

where m is the mass of the bullet and v is its initial velocity.

Equating the two expressions for internal energy, we get:

(1/2)mv² = mCΔT

Solving for v, we get:

v = √(2CΔT)

Substituting the given values, we get:

v = √(2 * 0.13 J/g°C * 100°C) = 0.234 km/s = 234 m/s

Therefore, the speed of the bullet just prior to striking the wall was 234 m/s (D).

A 200-G Lead Bullet Is Shot into a Wooden Wall ∘\circ∘

A 200-G Lead Bullet Is Shot into a Wooden Wall $\circ$