Mechanics

Linear Mechanics

100

Ally and Chris collide while rollerblading. Assuming friction is negligible, named a conserved physical quantity following their collision.

Linear Momentum, Velocity of Center of Mass, or Total Energy

200

Sylvia and Sam are floating in space. If Sam weights 105 kg and Sylvia weights 95 kg, how far is Sam from the center of mass if they are 4.8m apart?

m₁x = m₂(4.80-x)

x= 2.28m

300

2 balls are on a frictionless surface. Ball A (0.517 kg) moves towards ball B (0.685 kg) at 1.21 ms^-1. What is the velocity of the center of mass?

P_system = (m₁+m₂) v_com

_{Psystem = (0.517 + 0.685) vcom}

P_system = P_a + P_b

P_system = 0.517kg x 1.21 ms^-1 + 0

0.62557 = (0.517 + 0.685) v_com

v_com = 0.521ms^-1

400

A cyclist (55kg) is riding her bike (11kg) and moves her center of mass relative to the bike forward horizontally 13.2 cm. How far is the center of mass relative to the bike?

m₁x₁ = m₂x₂

11x = 55 (13.2-x)

x= 11cm

500

A pool ball  (0.146 kg) travelling at 9.00 ms^-1 is about to collide to with another ball (0.165 kg). What is the velocity of Center of Mass right before the collision? 

v_com = sum_momentum/sum_mass

v_com = (0.146*9.00)/0.146+0.165

v_com = 1.31/0.311

v_{com = 4.21ms}^-1

Circular Motion

100

Name the force that keeps a satellite in orbit

Force of gravity

200

Sam flies an airplane with a mass of 635kg, banking at 22.5^o . Calculate the vertical lift required for the plain to maintain altitude.

6230N

300

If the Earth weighs 5.97x10²⁴kg, calculate the force acting on a 300kg satellite 4.22 x 10⁷m away.

gravitational constant =

6.67408 × 10^-11 m3 kg-1 s-2

F_{g =} GMm/r²

F_g = 67.1N

400

If the Earth weighs 5.97x10²⁴kg, calculate the speed required for a 300kg satellite 4.22 x 10⁷m away to prevent it falling to the surface

gravitational constant =

6.67408 × 10^-11 m3 kg-1 s-2

3.07 x 10³ ms^-1

500

A child swings on a tire hanging from a vertical chain. He travels at 2.61 ms^-1 around radius of 4.11m. Assuming him and the swing weigh 70kg, what is the tension on the chain?

2.62ms^-1

Angular Mechanics

100

Assuming no friction, state the energy change that occurs when rolling a cylinder down a slope

Gravitational Potential --> Kinetic

200

State 100RPM in rad s^-1

10.5 rad s^-1

300

If a hollow cylinder has a radius of 0.058m rolls down the slope to a max speed 0.250ms^-1. If the rotational inertia is 1.40 kg m² what is the rotational kinetic energy? 

RKE = Iω²/2

=1.30J

400

The rotational inertia of a saw blade is 1.28 x 10 ^-3 kg m². If it takes 0.12s to accelerate the blade to full speed, how much power does the motor produce?

1108 W

500

A 76kg diver rotates as he dives off the high board. His rotational inertia is 3.73kgm². If his angular speed is 9.82 rad s^-1, what is his angular momentum?

36.6kgm²s^-1

Formula(not required to be memorized for exam)

100

Formula for kinetic energy

E_k = mv²/2

200

Formula for the Force of Gravity

F_g = GMm/r²

300

Formula for Angular Momentum

L = mvr

400

Formula for calculating position of Center of Mass

x_com = (m₁x_{1 +} m₂x₂)/(m₁₊m₂)

500

Formula for Angular Frequency

ω = 2πf

Units

100

3040km in m

3 040 000m

200

The prefix mega- denotes what?

10⁶

300

What symbol signifies a micro- unit?

µ

400

The prefix nano denotes what?

10^-6

500

What is the standard unit for mass in a momentum calculation?

kg