Instructor: Dr. Tatiana Erukhimova Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 16, 17, 18

2 or 3 D motion Definition of work: Kinetic energy: Work-energy theorem:

Work Energy Theorem

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Problem 2 p.122 A 3 slug mass is attached to a spring which is pulled out one foot. The spring constant k is 100 pounds/ft. How fast will the mass be moving when the spring is returned to its unstretched length? (Assume no friction.)

A 5. 00 kg block is moving at v0=6 A 5.00 kg block is moving at v0=6.00 m/s along a frictionless, horizontal surface toward a spring with constant k=500 N/m that is attached to a wall. Find the maximum distance the spring will be compressed. If the spring is to compress by no more than 0.150 m, what should be the maximum value of v0?

1) Plot the free body diagram for each of the blocks; Quiz Ch7 A block of mass m slides down on the larger block of mass M (see the figure below). There is non-zero coefficient of friction between the two blocks. Neglect the friction between the block of mass M and the table. 1) Plot the free body diagram for each of the blocks; 2) Find the work done by gravity on the block of mass m (the smaller one) in two coordinate systems shown above, if the height of the inclined plane is H. x y y

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How many joules of energy does 100 watt light bulb use per hour How many joules of energy does 100 watt light bulb use per hour? How fast would a 70-kg person have to run to have that amount of energy?

A car is stopped by a constant friction force that is independent of the car’s speed. By what factor is the stopping distance changed if the car’s initial speed is doubled?

Quiz Ch 7 (a) A block of mass m is attached to a spring, spring constant k, and is on a table with coefficient of friction . The spring is unstretched at x=0. m x=0 x=A x=B Find the work done by the spring and the work done by the table if the mass moves from A to B. Find the work done by the spring and work done by the table if the mass moves from B to A. Find the total work done by the spring for the round trip. Find the total work done by the table for the round trip.

Quiz Ch 7 (b) A block of mass M is on a horizontal surface and is attached to a spring, spring constant k. If the spring is compressed an amount A and the block released from rest, how far will it go before stopping if the coefficient of friction between the block and the surface is ? How will this answer change if the block is not attached to the spring?? Consider the spring force given by Fx = –kx+nx2 Consider  = 0 (1 + x/d).

Quiz A block of mass m is attached to a vertical spring, spring constant k. The spring is unstretched at y=0. A If the spring is compressed an amount A and the block released from rest, how high will it go?

James Prescott Joule b. Dec. 24, 1818, Salford, Lancashire, England d James Prescott Joule b. Dec. 24, 1818, Salford, Lancashire, England d. Oct. 11, 1889, Sale, Cheshire Discovered some basic laws of electricity and thermodynamics (Joule’s Law and Joule-Thomson Law); established the basis of the Law of Conservation of Energy and The First Law of Thermodynamics Main occupation and source of funding: Brewery

Since childhood, he was a fearless and meticulous experimenter Was home-schooled by some of the finest scientists of his time (including John Dalton) Since childhood, he was a fearless and meticulous experimenter As a boy, he hiked in the mountains with a pistol, studying echo and the speed of sound. He sounded the depth of Lake Windermere to be 198 ft. He tortured servants with crazy experiments. Spent his honeymoon climbing in French Alps and measuring the temperature at the top and the bottom of waterfalls

1843 (Age 24): Paddle-wheel experiment: mechanical work can be converted into heat! Therefore, heat is one of the forms of energy. It led to the First Law of Thermodynamics It also showed that energy is conserved. Energy Conservation Law! Met with hostility and disbelief. It took decades before Joule’s discovery was accepted. Only one person believed Joule. It was William Thomson (later Lord Kelvin). They started working together.

As a teenager, Joule was trying to replace steam engines with electric engines in his brewery. He failed, but became interested in the connections between mechanical work, heat, and electricity. In 1840, at the age of 21, he discovered “Joule’s Law”: Heat generated in a wire = Resistance x Current^2 It showed that electricity can be converted into heat!

All forces are CONSERVATIVE or NON-CONSERVATIVE

or A force is conservative if: The work done by the force in going from to is independent of the path the particle follows or The work done by the force when the particle goes from to around a closed path, back to , is zero.

Non-conservative: doesn’t satisfy the above conditions

If a force can be written as the derivative of some function, that force is conservative. 1D case: U(x) is called the potential energy function for the force If such a function exists, then the force is conservative

does NOT depend on path! 1D case:

does NOT depend on path! If Fx(x) is known, you can find the potential energy function as

Force of gravity: Potential energy function: Spring: Potential energy function:

Have a great day! Reading: Chapter 7 Hw: Chapter 7 problems and exercises