Ch.1 - Chemical Tools: Experimentation & Measurement

McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook

McMurry 8th Edition

Ch.1 - Chemical Tools: Experimentation & Measurement

Problem 78

Chapter 1, Problem 78

Which has more kinetic energy, a 1400 kg car moving at 115 km/h or a 12,000 kg truck moving at 38 km/h?

Verified step by step guidance

Step 1: Understand that kinetic energy (KE) is given by the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity. In this case, the masses are given in kilograms, but the velocities are given in km/h. We need to convert these velocities to m/s by multiplying by 1000/3600.

Step 2: Substitute the mass and velocity of the car into the kinetic energy formula. The mass (m) is 1400 kg and the velocity (v) is 115 km/h, which needs to be converted to m/s.

Step 3: Substitute the mass and velocity of the truck into the kinetic energy formula. The mass (m) is 12,000 kg and the velocity (v) is 38 km/h, which needs to be converted to m/s.

Step 4: Calculate the kinetic energy for both the car and the truck using the formula from step 1.

Step 5: Compare the two kinetic energies to determine which vehicle has more kinetic energy. The vehicle with the higher kinetic energy value has more kinetic energy.

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Key Concepts

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

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 0.5 * m * v², where m is mass and v is velocity. This means that both the mass of the object and its speed significantly influence its kinetic energy. Higher speeds and greater masses result in increased kinetic energy.

Units of Measurement

In physics, it is crucial to use consistent units when calculating quantities like kinetic energy. In this case, the mass is given in kilograms (kg) and the speed in kilometers per hour (km/h). To apply the kinetic energy formula correctly, speeds may need to be converted to meters per second (m/s) for standardization.

Comparison of Quantities

When comparing kinetic energies of different objects, it is essential to calculate each object's kinetic energy using the same formula and units. This allows for a direct comparison of their energies, helping to determine which object has more kinetic energy based on their respective masses and velocities.

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Assume that the kinetic energy of a 1400 kg car moving at 115 km/h (Problem 1.78) is converted entirely into heat. How many calories of heat are released, and what amount of water in liters could be heated from 20.0 °C to 50.0 °C by the car's energy? (One calorie raises the temperature of 1 mL of water by 1 °C)

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