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Worksheet 302

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.

Force (Newton's second law)
Mechanical Advantage - Law of Lever
Subtraction

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

Division

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/

Bearing capacity for square foundations (Terzaghi's Theory)

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the ... more

Bearing capacity for circular foundations (Terzaghi's Theory)

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the ... more

Bearing capacity for continuous foundations (Terzaghi's Theory)

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the ... more

Worksheet 316

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:

Force (Newton's second law)

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

Disk area

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 9×109 N/m2. Now,all quantities except ΔL are known. Thus:

Young's Modulus

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/

Low-density lipoprotein - Estimation of LDL particles via cholesterol content - in mmol/l

Low-density lipoprotein (LDL) is one of the five major groups of lipoproteins. These groups, from least dense to most dense, are: ... more

Low-density lipoprotein - Estimation of LDL particles via cholesterol content - in mg/dl

Low-density lipoprotein (LDL) is one of the five major groups of lipoproteins. These groups, from least dense to most dense, are: ... more

Nodal Precession

Nodal precession is the precession of an orbital plane around the rotation axis of an astronomical body such as Earth. This precession is due to the ... more

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