Homework Help: 2D Motion

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1. Package has same initial velocity as plane's velocity; since it is horizontal, no need to resolve into vertical and horizontal components. (a) Use free fall equations to find time. (b) use time from part a to find horizontal distance.
2. Again a horizontal initial velocity, but here we have the information to find the time in the horizontal dimension. Use speed and horizontal distance to find time. In that time, how far will something fall?
3. Here we have a launch angle other than horizontal. Find vertical and horizontal components of initial velocity. Here they are the same, but this won't always be the case. Using the vertical component, find the time for the flight. Now using the horizontal component, figure how far it will go in that much time.
4. Plug and chug
5. Here you have to calculate the speed of the earth as it orbits the sun: v = d/t
6.(a & b) Straight-ahead calculation of centripetal acceleration and force except for the units of the speed and the weight is given and not the mass. (c) To find the frictional force, you must realize just what it is that provides the centripetal force for the car to turn.
8. Remember, at the bottom of the circle the string must provide the centripetal force to make the stopper go in a circle plus support the weight of the stopper. At the top, the weight helps by providing some of the centripetal force.

10. First find radial distance from center of earth using earth's radius. Next, find value of g at this altitude. Now, plug into the equation for critical velocity because that's how fast satellites travel.

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1. 1 revolution = 2 pi radians; 1 radian = 57.3 degrees
2. See #1
3. Two answers here, one for the somersault dive and one for the twisting dive.
4. Look up the rotational inertia equation for a uniform sphere on p 105. Be careful with the units of the information given.
5. (a) Find change in angular velocity. (b) Use angular constant acceleration equations on page 103.
7. The force asked for is the force that creates the torque that changes the speed. Find the angular acceleration, then use 2nd law for rotation to find torque. Assume the merry-go-round is a disk for the rotational inertia. The applied force must be enough to create the torque plus overcome the frictional force. (325 N)

Page 124
7. Rotary work problem: calculate torque, multiply times angular displacement. Watch the units!
11. Rotary work must equal linear work in this case. Weight times height equals torque times angular displacement. Convert to revolutions.

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5. Assume the wheel is a thin ring. Refer to p. 105 for rotational inertia. Be sure all quantities are in fundamental units.
9. (a) Assume the earth is a solid sphere. Get the mass and radius from p. 66. Assume 1 day = 24 hours. Calculate angular speed in fundamental units. (b) Use 1.50 x 10¹¹ m as the radius of the earth's orbit.
10. (a) Ball has both rotary and linear kinetic energy. To find the rotary energy, use the rotational inertia for a solid sphere found on page 105. Express angular velocity in terms of linear velocity and radius. When rotational inertia and angular velocity spuared are multiplied together, the radius cancels out and is therefore not necessary for the problem. (b) Ball will roll up the incline until all kinetic energy is converted to potential energy. Set these quantities equal and solve for h. Remember, this is the vertical height, not the distance up the plane. Use trig to find the distance.