Question

A firearms company is testing a new model of rifle by firing a 7.50-g lead bullet into a block of wood having a mass of 17.5 kg. The bullet embeds into the block and the collision generates heat. As a consequence, the temperature rises by 0.040°C, as measured with a high-precision thermometer. Assuming that all the kinetic energy of the bullet goes into heating the system, what is the bullet’s speed when it enters the block? The initial temperatures of bullet and wooden block can be considered identical and the specific heats of lead and wood are c_Pb = 130 J/(kg ⋅ C°) and c_wood = 1700 J/(kg ⋅ C°), respectively.

Answer 1

Solution:

Given,

T = 0.04^o.

Find the heat energy due to temperature difference,

Q = m_pdc_pdT + m_woodc_woodT

= 0.0075*130*0.04 + 17.5*1700*0.04

= 0.039 + 1190

= 1190.039 J.

Given,

K.E = Q

1/2mv² = 1190.039

v² = 2*1190.039/7.5*10^-3

v = 563.333 m/s.

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