P2 Mechanics Part 2

7/30/2019 P2 Mechanics Part 2

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Physics Day 2Mechanics Part 2

Centripetal Force/Acceleration

r

vac

2

cmar

mvF

2

Work and Energy

FdW (only force component in the direction of motion)

Mechanical Energy

PEKEE 221 mvKE mghPE (gravitational)

Conservation of Mechanical Energy ( 0E )

ffii mghmvmghmv 22

2

1

2

1(if no work is done by nonconservative forces)

Work-Energy Theorem

EW (work performed by nonconservative forces; when mechanical energy is not conserved)

Power Fvt

W

P

Momentum and Impulse

Momentum mvp

Impulse-Momentum Theorem mvtF

Collisions

Elastic Collisions

...... 22112211 ffii vmvmvmvm

...2

1

2

1...

2

1

2

1 222

2

11

2

22

2

11 ffii vmvmvmvm

Perfectly Inelastic Collisions

(objects stick together)

fii vmmvmvm ...)(.. 212211

ac

v

v

ac

ac

v

Impulse


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Rotational Kinematics

Angular Displacement = or rd

Angular Velocityt

r v

Angular Accelerationt

a r

Rotational Kinematics Eqns Analagous Translational Kinematics Eqnst vtd (no acceleration)

tavg tvd avg (constant acceleration)

2

2

1tti

2

2

1attvd i (constant acceleration)

222

if advv if 222 (constant acceleration)

Rotational Dynamics

Center of Mass...

...

21

2211

mm

xmxmxCM Rotational/

Angular

Translationa

d

v

a

ITorque F lever arm m I (just like F=ma) F

2

21 IKE 2

21 mvKE

W FdW Inertia (for point masses about an axis)2mrI IL mvp

Angular Momentum IL

Rotational KE 2

2

1I


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In-Class ProblemsMechanics Part 2

1. A boy is twirling a 100g yoyo with a 600cm radius horizontally in a circle above his head with a speed of

2m/s. What is the centripetal force acting on the yoyo?

2. Give an expression for the radius of a satellite in a stable orbit around the Earth in terms of the gravitational

constant G, the mass of the Earth ME, and the velocity v of the satellite.

3. A roller coaster car completes a loop-d-loop on its track. Is the normal force acting on the car by the track

greater at the top or bottom of the loop-d-loop? By how much (answer in terms ofm, v, r, and g)?

4. How much work is performed by an Alaskan husky pulling a dog sled 10m across the snow with a pullingforce of 300N.

5. A ball is dropped from a 45m cliff. What is the velocity of the ball just before it reaches the ground (ignore

air resistance)?

6. A 1.5m long pendulum is released from an angle of 60 from the vertical. What is the maximum velocityachieved by the pendulum?

7. A 1kg ball is dropped from a 45m cliff. Its velocity just before it reaches the ground is 20m/s. How much

work is done by air resistance on the ball?

8. If John can do twice as much work as Bill in half the time, how much greater power is John providing?

9. A 1kg baseball traveling at 40m/s towards home is sent in the opposite direction at 30m/s after being hit witha baseball bat. If the bat is in contact with the ball for 0.05s, with what force was the ball struck by the bat?

10. A 2kg ball heading west at 5m/s across a frictionless surface collides head-on with a 4kg ball that had also

been moving. After the collision, the two balls are stuck together and are moving with a velocity of 5m/s

directly east. What was the original velocity of the 4kg ball?


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11. A stationery bomb explodes into 3 fragments. The 1st

fragment weighing 2kg is moving directly north witha velocity of 100m/s after the explosion. The 2

ndfragment weighing 4kg is moving directly west with a

velocity of 50m/s after the explosion. What is the velocity of the 3rd

fragment (weighing 2kg) immediately

after the explosion?

12. A fly is sitting on the edge of a record with a radius of 0.2m spinning at constant velocity. If the fly

completes 6 revolutions in 30s, what is the angular velocity of the record? What is the translational velocityof the fly?

13. A boy is riding a horse on a carousel located 2m from its center, while his father is sitting on a bench on the

carousel located 5m from its center. How much greater is the angular velocity of the boy compared to hisfather? How much greater is the translational velocity of the boy compared to his father?

14. Where would a fulcrum need to be placed for the following bar to be balanced perfectly?

15. A 20kg sign is hanging on the end of a 50kg boom that is suspended by a wire attached to the wall as in the

following figure. What is the tension in the cable?

16. A solid cylinder and a hollow cylinder of equal mass and radius roll down an incline. Which one reachesthe bottom first?

17. A wheel with a moment of inertia of 100kg.m

2is accelerated from rest by a motor to an angular velocity of

80rad/s. How much work is performed by the motor?

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P2 Mechanics Part 2