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Block and tackle - efficiency approximation - with friction factor

A block and tackle is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift or pull heavy loads.A more precise ... more

Block and tackle - efficiency approximation - without friction factor

f is the number of sheaves in the purchase, and there is a roughly % loss of efficiency at each sheave due to friction, then:

... more

Mechanical advantage - actual

Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves ... more

Mechanical Advantage - Meshing Gears

Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves ... more

Mechanical Advantage - Differential Pulley

Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves ... more

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/

Worksheet 341

The awe‐inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high (H), with a mass of about 7×10^9 kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging). Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hour days, 330 days per year.

a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.

Division
Potential energy

b) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps, bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 Kcal/hour.

first we calculate the number of hours worked per year.

Multiplication

then we calculate the number of hours worked in the 20 years.

Multiplication

Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.

Multiplication
Multiplication

The efficiency is the resulting potential energy divided by the consumed energy.

Division
Mechanical Advantage - Law of Lever

Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves ... more

Compound machines (efficiency)

A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that ... more

Compound machines (mechanical advantage)

A compound machine is a machine formed from a set of simple machines connected in series with the output force of one providing the input force to the ... more

Screw - mechanical advantage

A screw is a mechanism that converts rotational motion to linear motion, and a torque (rotational force) to a linear force. It is one of the six classical ... more

Hydraulic pump flow

A hydraulic pump is a mechanical sourse of power that converts mechanical power into hydraulic energy (hydrostatic energy i.e. flow, pressure). It ... more

Backlash (due to operating center modifications)

In mechanical engineering, backlash, sometimes called lash or play, is clearance or lost motion in a mechanism caused by gaps between the parts. It can be ... more

Backlash (due to tooth thickness changes)

In mechanical engineering, backlash, sometimes called lash or play, is clearance or lost motion in a mechanism caused by gaps between the parts. It can be ... more

Hydraulic pump power

A hydraulic pump is a mechanical sourse of power that converts mechanical power into hydraulic energy (hydrostatic energy i.e. flow, pressure). It ... more

Ball Screw - Driving Torque

A ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction. A threaded shaft provides a helical ... more

Tractive Force

As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total ... more

Thermodynamic efficiency (Rankine cycle)

Rankine cycle is a model that is used to predict the performance of steam engines. The Rankine cycle is an idealised thermodynamic cycle of a heat engine ... more

Time-domain reflectometry ( reflection coefficient-resistive load)

Time-domain reflectometry or TDR is a measurement technique used to determine the characteristics of electrical lines by ... more

Solar Cell Efficiency

Solar cell efficiency is the ratio of the electrical output of a solar cell to the incident energy in the form of sunlight. The energy conversion ... more

Tractive Force - Steam locomotives

As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total ... more

Energy of damped harmonic motion

Damped harmonic motion is a real oscillation, in which an object is hanging on a spring. Because of the existence of internal friction and air resistance, ... more

Ideal Transformer equation - Currents

A transformer is an electrical device that transfers energy between two circuits through electromagnetic induction. A transformer may be used as a safe and ... more

Ideal Transformer equation - Voltages

A transformer is an electrical device that transfers energy between two circuits through electromagnetic induction. A transformer may be used as a safe and ... more

Miles Equation

In 1954, Miles developed his version of this equation for GRMS as he was researching fatigue failure of aircraft structural ... more

Engine displacement

Engine displacement is the volume swept by all the pistons inside the cylinders of a reciprocating engine in a single movement from top dead centre (... more

Specific Impulse by weight - with mass flow rate

Specific impulse (usually abbreviated Isp) is a measure of the efficiency of rocket and jet engines. By definition, it is the impulse delivered per unit of ... more

Solar Cell - Fill Factor

Solar cell efficiency is the ratio of the electrical output of a solar cell to the incident energy in the form of sunlight. The energy conversion ... more

Specific Impulse by weight

Specific impulse (usually abbreviated Isp) is a measure of the efficiency of rocket and jet engines. By definition, it is the impulse delivered per unit of ... more

Isentropic Relations for an Ideal Gas - Temperature and Pressure

In thermodynamics, an isentropic process is an idealized thermodynamic process that is adiabatic and in which the work transfers of the system are ... more

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