Skip to main content
Ch 17: Temperature and Heat
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 17, Problem 32

A nail driven into a board increases in temperature. If we assume that 60% of the kinetic energy delivered by a 1.80 kg hammer with a speed of 7.80 m/s is transformed into heat that flows into the nail and does not flow out, what is the temperature increase of an 8.00 g aluminum nail after it is struck ten times?

Verified step by step guidance
1
First, calculate the kinetic energy (KE) of the hammer using the formula: \( KE = \frac{1}{2}mv^2 \), where \( m = 1.80 \text{ kg} \) and \( v = 7.80 \text{ m/s} \).
Determine the total kinetic energy delivered to the nail after ten strikes by multiplying the kinetic energy of one strike by ten.
Calculate the amount of energy converted to heat using the given efficiency: 60% of the total kinetic energy. This is done by multiplying the total kinetic energy by 0.60.
Use the formula for heat transfer to find the temperature increase: \( Q = mc\Delta T \), where \( Q \) is the heat energy, \( m = 0.008 \text{ kg} \) is the mass of the nail, and \( c = 900 \text{ J/(kg} \cdot \text{°C)} \) is the specific heat capacity of aluminum.
Rearrange the formula to solve for the temperature increase \( \Delta T \): \( \Delta T = \frac{Q}{mc} \). Substitute the values for \( Q \), \( m \), and \( c \) to find \( \Delta T \).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
7m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, calculated using the formula KE = 0.5 * m * v^2, where m is the mass and v is the velocity. In this problem, the kinetic energy of the hammer is partially converted into heat, which affects the temperature of the nail.
Recommended video:
Guided course
06:07
Intro to Rotational Kinetic Energy

Heat Transfer

Heat transfer is the process of energy moving from one body or system to another due to a temperature difference. Here, 60% of the hammer's kinetic energy is converted into heat, which is absorbed by the nail, leading to an increase in its temperature.
Recommended video:
Guided course
05:14
Overview of Heat Transfer

Specific Heat Capacity

Specific heat capacity is the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius. For aluminum, this value is crucial to determine how much the temperature of the nail increases when it absorbs the heat generated by the hammer's impact.
Recommended video:
Guided course
06:50
Specific Heat & Temperature Changes
Related Practice
Textbook Question

In very cold weather a significant mechanism for heat loss by the human body is energy expended in warming the air taken into the lungs with each breath. On a cold winter day when the temperature is -20°C, what amount of heat is needed to warm to body temperature (37°C) the 0.50 L of air exchanged with each breath? Assume that the specific heat of air is 1020 J/kg K and that 1.0 L of air has mass 1.3 × 10-3 kg.

1
views
Textbook Question

One suggested treatment for a person who has suffered a stroke is immersion in an ice-water bath at 0°C to lower the body temperature, which prevents damage to the brain. In one set of tests, patients were cooled until their internal temperature reached 32.0°C. To treat a 70.0 kg patient, what is the minimum amount of ice (at 0°C) you need in the bath so that its temperature remains at 0°C? The specific heat of the human body is 3480 J/kg C°, and recall that normal body temperature is 37.0°C.

1
views
Textbook Question

A blacksmith cools a 1.20 kg chunk of iron, initially at 650.0°C, by trickling 15.0°C water over it. All of the water boils away, and the iron ends up at 120.0°C. How much water did the blacksmith trickle over the iron?

2
views
Textbook Question

While painting the top of an antenna 225 m in height, a worker accidentally lets a 1.00-L water bottle fall from his lunchbox. The bottle lands in some bushes at ground level and does not break. If a quantity of heat equal to the magnitude of the change in mechanical energy of the water goes into the water, what is its increase in temperature?

Textbook Question

In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in 0.320 kg of water. How much time is required? Assume that all of the heater's power goes into heating the water.

1
views
Textbook Question

You have 750 g of water at 10.0°C in a large insulated beaker. How much boiling water at 100.0°C must you add to this beaker so that the final temperature of the mixture will be 75°C?

2
views