Newton's Law of Universal Gravitation

Newton's Law of Universal Gravitation

OBJECTIVES

• Apply the concept of gravitational potential energy in solving problems

Open Ended

How do you determine if work is done upon an object?

Work is done upon an object if:

• there is force involved upon the object that makes it displaced from its initial position

• if that object gains energy and the energy acquired by an object upon which work is done is known MECHANICAL ENERGY

Mechanical Energy

• energy possessed by an object due to its motion (kinetic energy)

• energy possessed by an object due to its position (potential energy)

Mechanical Energy as the ability to do work

• Any object that possesses mechanical energy - whether it is in the form of potential energy or kinetic energy - is able to do work.

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A classic example involves the massive wrecking ball of a demolition machine. The wrecking ball is a massive object that is pulled to a high position and allowed to swung and hit into the building structure or other object in order to demolish it. The operator releases the wrecking ball at highest point and creates the right amount of force.

The work performed by the wrecking ball depends on:

• weight or force

• height/position with respect to the ground

Remember W = Fd

• since F = mg

• and d = change in height, ( Δh)

• so W = (mg)( Δh)

The more work to perform and energy stored in the wrecking ball, the higher the wrecking ball from the ground.

Gravitational Potential Energy, E_g

• is the energy stored of an object because of its distance above the surface of the Earth

The change in gravitational potential energy of an object is expressed as: E_g = mgΔh

• m – is the mass of the object in kilograms

• g – is the acceleration due to gravity at 9.8 m/s²

• Δh – is the vertical displacement of the object in meters

• ΔE_g - is the object’s change in gravitational potential energy in Joules  

Open Ended

A crane lifts an I-beam to a height of 30 meters, giving it a potential energy of 108, 486 J. What is the mass of the I-beam?

Open Ended

A 150 g textbook is sitting on a 1.20 m table. If the textbook is lifted 0.8 m above the table, how much gravitational potential energy does it have:

A.) with respect to the table?

B.) with respect to the ground?

Open Ended

A given mass 1.2 kg is lifted Δh = 28 m above the ground, find the ΔE_g.

Open Ended

A 20 kg mass is pushed by a force in an inclined ramp 30 degrees with the horizontal that makes it slide up form lowest point to highest point of the ramp. The ramp is 5 m long. A.) Find the height of the ramp. B.) What is the total amount of gravitational potential energy gained by the mass? Assume there is no frictional force in the system.