PY 205, Spring 2022, Exam 3 Review

Kinetic Energy

100

What is the equation to find the center of mass of a mutli-particle system?

r_CM=m₁r₁ + m₂r₂ + .... / M_total

pg. 350

200

What is the translational kinetic energy of a spinning 140 g Frisbee that is traveling at a speed of 15 m/s? Is this the total kinetic energy of the Frisbee?

K_trans= 15.8 J

pg. 351

300

What is the moment of inertia of a bicycle wheel? (Hint: A bicycle wheel has most of its mass M located in the outer rim)

I = MR²​

pg. 355

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400

Describe a system that has the moment of inertia 

I = 1/12 ML² + 1/4MR²

A cylinder of Length L, radius R, rotating about an axis perpendicular to the cylinder through the center of the cylinder.

500

A thin rod with mass 140 g and 60 cm long rotates at an angular speed of 25 rad/s about an axle that is 20 cm from one end of the rod.  What is its kinetic energy?

K_tot = 1.75 J

Pg. 259

Collisions

100

The difference between an elastic and inelastic collision is...

In an elastic colision, the internal energy does not change whereas in an inelastic collision, energy is lost to heat, deformation, rotation, vibration, etc.

200

What is a maximally inelastic collision?

A collision in which there is maximum dissipation.  Therefore, a maximally inelastic collision is one where the combined momentum before and after the collision is 0.

Before, opposite direction equal magnitude

After, at rest

Pg. 385-386

300

Cart 1 collides with stationary cart 2, which is identical.  Suppose that the collision is (nearly) elastic.  In this case, there is the final momenta of the two carts?

2 p_1x,f p_2x,f = 0

pg. 387

400

Consider a maximally inelastic collision of two carts, one initially at rest.  That means the carts stick together and each haas the same momentum p_1xf = p_2xf.  Final the final momentum and final speed of the carts in terms of there initial values.

p_1xf + p_2xf = p_1xi

2p_1xf = p_1xi

p_1xf = 1/2p_1xi

v_f = 1/2 v_i

_{pg. 388}

500

In an orbiting spacecraft a Ping-Pong ball of mass m travelling in the +x diretion with an initial momentum of p_1i hits  a stationary bowling ball of mass M head on.  What is the momentum after the collision?

-p_1f - p_1i = 2p_1i

Angular Momentum

100

What is the definition of angular momentum?

L_trans,A = r_A x p

|L_trans,A| = |r||p|sin theta

pg.  421

200

What is the definition of cross product?

A x B = <A_yB_z - A_zB_y, A_zB_x - A_xB_z, A_xB_y - A_yB_x>

pg. 420

300

What is the direction of transnational angular momentum of a comet orbiting the sun clockwise in the xz-plane?

-y

pg. 418

400

A bicycle wheel has a mass of 0.8 kg and a radius of 32 cm.  If the wheel rotates in the xz plane, spinning clockwise when viewed from the +y axis, and making one revolution every 0.75 s, what is the rotational angular momentum of the wheel?

L_rot = <0, -0.69, 0> kg m²/s

pg. 423

500

Given that K_rot = 1/2Iw² and L_rot = Iw_, how can you write K_rot in terms of L_rot?

K_rot = L²_rot / 2I

pg. 424

Torque

100

What changes the angular momentum of a system?

Torque

pg. 426

200

What is the definition of torque?

tau_A = r_A x F

pg. 426

300

The net torque on a seesaw is <0, 0, -117.6> Nm.  Apply the angular momentum principle.  Will the seesaw rotate clockwise or counterclockwise?

Clockwise

L_f,A = <0, 0, -47.0> kg m²/s

pg. 429

400

Two people sit on a seasaw.  The person on the left has a mass M₁ = 90 kg and sits at a distance d₁ = 1.2 m from the nearly friction-less axle.  The person on the right has a mass M₂ = 40 kg.  Where must the person on the right sit in order that the seasaw will not rotate?  The seesaw has negligible mass.

2.7 m

pg. 442-443

500

A wheel of radius R and moment of inertia I is mounted on a low-friction axle.  A string is wrapped around the edge and you pull it with a force F.  At a certain time the angular speed if w_i.  After a time interval dt, what is the angular speed w_f?

w_f = w_i + RFdt / I

pg. 434 - 444

Internal Energy and Heating

100

Internal energy refers to the energy of....

The systems vibration energy, rotational energy, thermal energy, chemical energy, etc.

200

The equation for specific heat on a per gram basis is...

C = dE_thermal / m dT

pg. 295

300

When Q is negative, what is the direction of energy transfer?

Energy transfer is out of the system because the energy is decreased.  

400

You stir 12-kg of water vigorously, doing 36,000-J of work.  If the container is well insulated , what temperature rise would you expect?

0.7 K

pg. 295-296

500

An electric heater recieves an energy input of 5000-J of electric energy.  During this time the heating element is maintained at a constant high temperature.  What is the change in thermal energy for the heater?  What is Q?

Q is the energy transfer between the heaters hot heating element and the cooler air.

dE_thermal = 0 J

Q = -5000 J

Pg. 299