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Chapter 5: Problem 21

Identify the force present, and explain whether work is being performed in the following cases: (a) You lift a pencil off the top of a desk. (b) A spring is compressed to half its normal length.

Short Answer

Expert verified
In case (a), the force present is gravity and the force exerted by your hand. Work is being performed since the applied force and the displacement are in the same direction (upward). In case (b), the force present is the spring force and the compression force. Work is being performed since the applied force and the displacement are in the same direction.

Step by step solution

01

Case (a): Lifting a pencil off the top of a desk

In this situation, the acting forces are the gravitational force (weight) acting on the pencil due to Earth's gravity, and the force exerted by your hand to lift the pencil. When you lift the pencil, you apply a force against gravity, causing displacement in an upward direction. Since the force applied (your hand) and the displacement of the pencil are in the same direction (upward), work is being performed.
02

Case (b): A spring is compressed to half its normal length

In this case, when you compress a spring, it exerts a force opposite to the direction of compression, which is the spring force. The force you apply to compress the spring is in the same direction as the displacement of the spring's individual molecules (i.e., they move closer together). As the force applied (compression force) and the displacement of the spring are in the same direction, work is being performed on the spring. To summarize: 1. In case (a), lifting a pencil off the top of a desk, the forces are gravity and the force exerted by your hand. Work is being performed as the force and displacement are in the same direction. 2. In case (b), compressing a spring to half its normal length, the forces are the spring force and the compression force. Work is being performed as the force and displacement are in the same direction.

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Most popular questions from this chapter

(a) When a 0.235-g sample of benzoic acid is combusted in a bomb calorimeter, the temperature rises \(1.642^{\circ} \mathrm{C}\). When a 0.265-g sample of caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{O}_{2} \mathrm{~N}_{4}\), is burned, the temperature rises \(1.525^{\circ} \mathrm{C}\). Using the value \(26.38 \mathrm{~kJ} / \mathrm{g}\) for the heat of combustion of benzoic acid, calculate the heat of combustion per mole of caffeine at constant volume. (b) Assuming that there is an uncertainty of \(0.002^{\circ} \mathrm{C}\) in each temperature reading and that the masses of samples are measured to \(0.001 \mathrm{~g}\), what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?

Identify the force present, and explain whether work is done when (a) a positively charged particle moves in a circle at a fixed distance from a negatively charged particle; (b) an iron nail is pulled off a magnet.

Two solid objects, \(\mathrm{A}\) and \(\mathrm{B}\), are placed in boiling water and allowed to come to temperature there. Each is then lifted out and placed in separate beakers containing \(1000 \mathrm{~g}\) water at \(10.0{ }^{\circ} \mathrm{C}\). Object \(\mathrm{A}\) increases the water temperature by \(3.50^{\circ} \mathrm{C} ; \mathrm{B}\) increases the water temperature by \(2.60^{\circ} \mathrm{C}\). (a) Which object has the larger heat capacity? (b) What can you say about the specific heats of A and B?

Methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) is used as a fuel in race cars. (a) Write a balanced equation for the combustion of liquid methanol in air. (b) Calculate the standard enthalpy change for the reaction, assuming \(\mathrm{H}_{2} \mathrm{O}(g)\) as a product. (c) Calculate the heat produced by combustion per liter of methanol. Methanol has a density of \(0.791 \mathrm{~g} / \mathrm{mL}\) (d) Calculate the mass of \(\mathrm{CO}_{2}\) produced per \(\mathrm{kJ}\) of heat emitted.

Given the data $$ \begin{aligned} \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)-\cdots+2 \mathrm{NO}(g) & \Delta H=+180.7 \mathrm{~kJ} \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \cdots-\rightarrow 2 \mathrm{NO}_{2}(g) & \Delta H=-113.1 \mathrm{~kJ} \\ 2 \mathrm{~N}_{2} \mathrm{O}(g)-\cdots 2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g) & \Delta H=-163.2 \mathrm{~kJ} \end{aligned} $$ use Hess's law to calculate \(\Delta H\) for the reaction $$ \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \stackrel{-\cdots} 3 \mathrm{NO}(g) $$
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