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Acceleration, in physics, is the rate at which the velocity of an object changes over time. Mathematically, instantaneous acceleration—acceleration over an ... more

The first image shows how helicopters store large amounts of rotational kinetic energy in their blades. This energy must be put into the blades before takeoff and maintained until the end of the flight. The engines do not have enough power to simultaneously provide lift and put significant rotational energy into the blades.

The second image shows a helicopter from the Auckland Westpac Rescue Helicopter Service. Over 50,000 lives have been saved since its operations beginning in 1973. Here, a water rescue operation is shown. (credit: 111 Emergency, Flickr)

Strategy

Rotational and translational kinetic energies can be calculated from their definitions. The last part of the problem relates to the idea that energy can change form, in this case from rotational kinetic energy to gravitational potential energy.

Solution for **(a)**

We must convert the angular velocity to radians per second and calculate the moment of inertia before we can find **E _{r}** . The angular velocity

**ω**for

**1 r.p.m**is

and for **300 r.p.m**

The moment of inertia of one blade will be that of a thin rod rotated about its end.

The total I is four times this moment of inertia, because there are four blades. Thus,

and so The rotational kinetic energy is

Solution for **(b)**

Translational kinetic energy is defined as

To compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy. This ratio is

Solution for **(c)**

At the maximum height, all rotational kinetic energy will have been converted to gravitational energy. To find this height, we equate those two energies:

Discussion

The ratio of translational energy to rotational kinetic energy is only **0.380**. This ratio tells us that most of the kinetic energy of the helicopter is in its spinning blades—something you probably would not suspect. The **53.7 m** height to which the helicopter could be raised with the rotational kinetic energy is also impressive, again emphasizing the amount of rotational kinetic energy in the blades.

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.

http://openstaxcollege.org/textbooks/college-physics

Creative Commons License : http://creativecommons.org/licenses/by/3.0/

In astrodynamics, the vis viva equation, also referred to as orbital energy conservation equation, is one of the fundamental equations that govern the ... more

Power is the rate at which work is done. It is equivalent to an amount of energy consumed per unit time. Power in mechanical systems is the combination of ... more

Centripetal force (from Latin centrum “center” and petere “to seek”) is a force that makes a body follow a curved path: its ... more

Water hammer (or, more generally, fluid hammer) is a pressure surge or wave caused when a fluid (usually a liquid but sometimes also a gas) in motion is ... more

Calculate the change in length of the upper leg bone (the femur) when a **70.0 kg** man supports **62.0 kg** of his mass on it, assuming the bone to be equivalent to a uniform rod that is **45.0 cm** long and **2.00 cm** in radius.

Strategy

The force is equal to the weight supported:

and the cross-sectional area of the upper leg bone(femur) is:

To find the change in length we use the Young’s modulus formula. The Young’s modulus reference value for a bone under compression is known to be **9×10 ^{9} N/m^{2}**. Now,all quantities except

**ΔL**are known. Thus:

Discussion

This small change in length seems reasonable, consistent with our experience that bones are rigid. In fact, even the rather large forces encountered during strenuous physical activity do not compress or bend bones by large amounts. Although bone is rigid compared with fat or muscle, several of the substances listed in Table 5.3(*see reference below*) have larger values of Young’s modulus Y . In other words, they are more rigid.

**Reference:**

This worksheet is a modified version of Example 5.4 page 188 found in :

OpenStax College,College Physics. OpenStax College. 21 June 2012.

http://openstaxcollege.org/textbooks/college-physics

Creative Commons License : http://creativecommons.org/licenses/by/3.0/

In the wheelbarrow of the following figure the load has a perpendicular lever arm of **7.50 cm**, while the hands have a perpendicular lever arm of **1.02 m**.**(a)** What upward force must you exert to support the wheelbarrow and its load if their combined mass is **45.0 kg**? **(b)** What force does the wheelbarrow exert on the ground?

**(a)** In the case of the wheelbarrow, the output force or load is between the pivot and the input force. The pivot is the wheel’s axle. Here, the output force is greater than the input force. Thus, a wheelbarrow enables you to lift much heavier loads than you could with your body alone. **(b)** In the case of the shovel, the input force is between the pivot and the load, but the input lever arm is shorter than the output lever arm. The pivot is at the handle held by the right hand. Here, the output force (supporting the shovel’s load) is less than the input force (from the hand nearest the load), because the input is exerted closer to the pivot than is the output.

Strategy

Here, we use the concept of mechanical advantage.

Discussion

An even longer handle would reduce the force needed to lift the load. The MA here is:

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.

http://openstaxcollege.org/textbooks/college-physics

Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Acceleration, in physics, is the rate of change of velocity of an object. An object’s acceleration is the net result of any and all forces acting on ... more

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A typical small rescue helicopter, like the one in the Figure below, has four blades, each is

4.00 mlong and has a mass of50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length. The helicopter has a total loaded mass of1000 kg.(a)Calculate the rotational kinetic energy in the blades when they rotate at300 rpm.(b)Calculate the translational kinetic energy of the helicopter when it flies at20.0 m/s, and compare it with the rotational energy in the blades.(c)To what height could the helicopter be raised if all of the rotational kinetic energy could be used to lift it?