Chapter 5: Problem 24

In Example \(5.3\), is it really necessary to know the mass of the concrete block to solve this problem? Put another way, would the answer be different if it was a 10 -kg block that was dropped instead of a 5 -kg one?

Short Answer

Expert verified

Would a 10-kg block give a different result than a 5-kg block? Answer: No, it is not necessary to know the mass of the concrete block to solve the problem in Example 5.3. The final velocity only depends on the height from which the block was dropped and the acceleration due to gravity. Therefore, the answer would not be different if it was a 10-kg block dropped instead of a 5-kg one.

Step by step solution

Recall the problem in Example 5.3

In Example 5.3, we were asked to find how fast a concrete block moving downward would be going at a certain distance from the point it was dropped, without considering air resistance.

Identify the relevant physical principle

To analyze this problem, we will use the principle of conservation of energy, specifically potential and kinetic energy. The gravitational potential energy (PE) converts to kinetic energy (KE) as the block falls.

Write down the energy conservation equation

Using the conservation of energy principle, we can write the equation as: PE_initial + KE_initial = PE_final + KE_final

Define the potential and kinetic energies for the block

Recall the equations for gravitational potential energy (PE) and kinetic energy (KE): PE = m * g * h KE = (1/2) * m * v^2 where m represents the mass of the block, g is the acceleration due to gravity (9.81 m/s²), h is the height, and v is the velocity of the block.

Plug in the energy equations to the conservation equation

Now let's plug the potential and kinetic energy equations into the conservation equation: m * g * h_initial + 0 = 0 + (1/2) * m * v_final^2 Notice that the initial kinetic energy is zero, and the final potential energy is zero.

Solve for the final velocity

Rearranging the equation and solving for the final velocity (v_final): v_final^2 = 2 * g * h_initial Taking the square root of both sides: v_final = sqrt(2 * g * h_initial)

Verify if the mass is needed to find the final velocity

As we can see from the final equation for v_final, the mass of the block does not appear in the equation. Therefore, it is not necessary to know the mass of the concrete block to solve the problem in Example 5.3.

Conclude the answer

In conclusion, knowing the mass of the concrete block is not necessary to solve the problem in Example 5.3, and the answer would not be different if it was a 10-kg block dropped instead of a 5-kg one. The final velocity only depends on the height from which the block was dropped and the acceleration due to gravity.

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In Example \(5.3\), is it really necessary to know the mass of the concrete block to solve this problem? Put another way, would the answer be different if it was a 10 -kg block that was dropped instead of a 5 -kg one?

Short Answer

Step by step solution

Recall the problem in Example 5.3

Identify the relevant physical principle

Write down the energy conservation equation

Define the potential and kinetic energies for the block

Plug in the energy equations to the conservation equation

Solve for the final velocity

Verify if the mass is needed to find the final velocity

Conclude the answer

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