A 1.17 kg hammer strikes a 20 g brass nail into a wood board. The nail is horizontally aligned and at the moment of impact with the nail, the hammer had a speed of 9.1 m/s. Assume both the hammer and the nail come to a stop and that all of the thermal energy generated goes into heating the nail. Determine how much the temperature of the nail will increase after one hit and how many hits it will take to increase its temperature 88°CΔT after one hit =Minimum number of hits needed to increase the temperature by at least 88°C = ### Specific Heat of Materials#### Solids- **Aluminum:** 921 J/kg·K- **Brass:** 402 J/kg·K- **Copper:** 377 J/kg·K- **Glass:** 840 J/kg·K- **Gold:** 126 J/kg·K- **Ice:** 2095 J/kg·K- **Iron:** 461 J/kg·K- **Lead:** 130 J/kg·K- **Nickel:** 502 J/kg·K- **Silver:** 239 J/kg·K- **Styrofoam:** 1131 J/kg·K- **Zinc:** 390 J/kg·K#### Liquids- **Acetone:** 2150 J/kg·K- **Benzene:** 1800 J/kg·K- **Bromine:** 470 J/kg·K- **Ethyl alcohol:** 2400 J/kg·K- **Gasoline:** 2220 J/kg·K- **Glycerin:** 2430 J/kg·K- **Kerosene:** 2010 J/kg·K- **Mercury:** 140 J/kg·K- **Olive oil:** 1970 J/kg·K- **Petroleum:** 2130 J/kg·K- **Toluene:** 1720 J/kg·K- **Water:** 4186 J/kg·K### ExplanationThis table displays the specific heat capacity of various materials, divided into solids and liquids. Specific heat capacity is the amount of heat required to change the temperature of 1 kilogram of a material by 1 Kelvin (or Celsius).- **Solids:** Generally have lower specific heat capacities compared to liquids, with values ranging from 126 J/kg·K for gold to 1131 J/kg·K for styrofoam. - **Liquids:** Typically have higher specific heat capacities. Water has the highest specific heat capacity in the list, at 4186 J/kg·K, making it very effective at storing thermal energy. These values are important in understanding thermal properties of materials, which are crucial in applications involving heat exchange and thermal management.

Given: Mass of hammer,mh=1.17kgMass of brass nail,mn=20g=20×10-3kgInitial Velocity of the hammer,uh=9.1m/sSpecific heat of Brass,C=402J/kg·K Assume that the change in the temperature of the nail in the one-hit is the change in temperature. Apply conservation of the energy, Kinetic energy is equal to heat energy that would raise the temperature of the brass nail i.e., K.E.=Q .... (1) The kinetic energy is: K.E.=12mhuh2 The heat energy is Q=mnC∆T Substitute the value of Kinetic energy and heat energy in equation (1). 12mhuh2=mnC∆T∆T=12mhuh2mnC .... (2)Substitute the value in equation (2). ∆T=121.17kg9.1m/s220×10-3kg402J/kg·K∆T=48.44kgm2/s28.04J/K∆T=48.44J8.04J/K∆T=6.02K The increase in the temperature of the nail in each hit is 6.02K. The minimum number of hits needed to increase the temperature by at least 88 degrees Celsius is: N=88∆TN=88K6.02KN=14 hits The minimum number of hits needed to increase the temperature by at least 88 degrees Celsius is by 14 hits.

Science

Advanced Physics

A 1.17 kg hammer strikes a 20 g brass nail into a wood board. The nail is horizontally aligned and at the moment of impact with the nail, the hammer had a speed of 9.1 m/s. Assume both the hammer and the nail come to a stop and that all of the thermal energy generated goes into heating the nail. Determine how much the temperature of the nail will increase after one hit and how many hits it will take to increase its temperature 88°C ΔT after one hit = Minimum number of hits needed to increase the temperature by at least 88°C

A 1.17 kg hammer strikes a 20 g brass nail into a wood board. The nail is horizontally aligned and at the moment of impact with the nail, the hammer had a speed of 9.1 m/s. Assume both the hammer and the nail come to a stop and that all of the thermal energy generated goes into heating the nail. Determine how much the temperature of the nail will increase after one hit and how many hits it will take to increase its temperature 88°C ΔT after one hit = Minimum number of hits needed to increase the temperature by at least 88°C

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