Posted on Categories:Thermodynamics, 热力学, 物理代写

# 物理代写|热力学代写Thermodynamics代考|Working with springs

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## 物理代写|热力学代写Thermodynamics代考|Working with springs

Springs have been used to store energy and do work for a long time although they’re generally used for doing small bits of work like running a clock, a wristwatch, or a wind-up toy. Work is defined by applying a force over a distance. When you push on a linear spring or twist a spiral spring, you apply work to do work on the spring. The spring is able to store energy until it’s released for doing work.

You may have noticed that when you push against a spring, the force increases with the amount the spring compresses. A material property called the spring constant $(k)$ determines how much force $(F)$ is required to compress or stretch a spring by a distance $(x)$. You calculate the force with the following equation:
$$F=k \cdot x$$
The units for each term in this equation are force in kilonewtons (kN), spring constant in kilonewtons per meter $(\mathrm{kN} / \mathrm{m})$, and distance in meters $(\mathrm{m})$.
$$W_{\text {spring }}=\int F d x=\frac{1}{2} k\left(x_2^2-x_1^2\right)$$
Figure $4-2$ shows that $x_1$ and $x_2$ are the initial and final positions of the spring relative to the relaxed length of the spring. The spring is at the relaxed length when the force on it equals zero. If the work starts with the spring at the relaxed position, then $x_1$ is zero. The units of work are in kilojoules (kJ).

## 物理代写|热力学代写Thermodynamics代考|Turning a shaft

A shaft is the most common way of putting work into motion. An automobile engine has pistons that are connected to a crankshaft that converts the reciprocating motion of the pistons into rotary motion used by the tires. A jet engine has a shaft that connects a turbine to a compressor so the turbine can turn the compressor. An electric motor has a shaft that rotates to do all kinds of work, like operating an elevator or mixing cake batter.
A shaft does not create work; it only carries work with rotary motion. The work carried by a shaft still uses a force moving over a distance. Figure 4-3 shows a perpendicular force $(F)$ applied to a shaft at the radius $(r)$ from the center axis to create torque $(T)$.

The torque on a shaft is related to the force by this equation:
$$T=F, r$$
The units for torque are newton-meters, force is expressed in newtons, and the radius is expressed in meters. The radius of the applied force is not the distance used in determining the work carried by the shaft. The work disof rotations $(n)$ turned by the shaft. The work distance is calculated using this equation:
$$s=(2 \pi r) n$$

The work transmitted by a shaft ( $W_{\text {shaft }}$ ) is calculated using the torque and the distance with this equation:
$$W_{\text {shaft }}=F \cdot s=(T / r)(2 \pi r) n=2 \pi \cdot n \cdot T$$
The units of work are kilojoules, so you have to use the following unit conversion in this equation:
$$1 \mathrm{~kJ}=1,000 \mathrm{~N} \cdot \mathrm{m}$$

## 物理代写|热力学代写Thermodynamics代考|Working with springs

$$F=k \cdot x$$

$$W_{\text {spring }}=\int F d x=\frac{1}{2} k\left(x_2^2-x_1^2\right)$$

## 物理代写|热力学代写Thermodynamics代考|Turning a shaft

$$T=F, r$$

$$s=(2 \pi r) n$$

$$W_{\text {shaft }}=F \cdot s=(T / r)(2 \pi r) n=2 \pi \cdot n \cdot T$$

$$1 \mathrm{~kJ}=1,000 \mathrm{~N} \cdot \mathrm{m}$$

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