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Children are playing with a rope that is tied to a branch and they sue it to swing out over a lake. The starting point of the swing is 3 m above the water and at the lowest point of the swing they are just few centimeters about the water. As they continue the swing they reach the highest point again and let go, falling into the water.

a) At which point in their motion will their centripetal acceleration be the greatest? Explain.

b) What is their acceleration just as they let go of the swing?

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A car is moving around a circular race track at 40 m/s in a clockwise direction. At one instant it is headed due east. In what direction is the acceleration of the car?

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A cargo plane is delivering to a South Pole research station. Flying horizontally at a height of 80 m, the pilot releases a package (drops out of plane) when they are 200 m (horizontally) from the target. If the package lands on the target, how fast war the plane moving when the package was dropped?

**Theres more, but i can figure out or learn how to do these, I could probably learn how to do the others.

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Children are playing with a rope that is tied to a branch and they sue it to swing out over a lake. The starting point of the swing is 3 m above the water and at the lowest point of the swing they are just few centimeters about the water. As they continue the swing they reach the highest point again and let go, falling into the water.

a) At which point in their motion will their centripetal acceleration be the greatest? Explain.

b) What is their acceleration just as they let go of the swing?

(a)

Circular Motion: Maintained by centripetal (centrally directed) force. The radius of motion, speed, and centripetal force are related by F = m*v^2/R

For the swinging rope problem, figure out which variables (of F, m, v, and R) can change (assume simplest motion satisfying given information) as a child is swinging.

After figuring out which variables stay the same and which change, try to obtain an understanding about how these variables change during the swing.

For example, where in the swing is a particular variable (e.g. v = speed) maximized (the start, the middle above the water, the end before letting go, ... etc).

Remember that F is the NET force which is the sum of all forces you can think of (gravity, rope, ... etc).

Your goal is to find out where in the swing F is maximized. You can figure this out by knowing where in the swing the other variables that change are maximized and then applying F = m*v^2/R.

(b)

When the swing is released, think about what forces are still acting on the child. Figure out what the net force is, and then you can get the acceleration through F = m*a (there is a special type of force which gives constant acceleration regardless of mass, so you don't necessarily need to know the mass of the child).

A car is moving around a circular race track at 40 m/s in a clockwise direction. At one instant it is headed due east. In what direction is the acceleration of the car?

Steady circular motion always requires a force directed towards the center of the circular path.

If you know the car is moving clockwise and is moving precisely east, you can pinpoint where exactly where the car is on the circular track.

Imagine you marking this point on a map with North, South, East and West directions.

The answer is then just the direction of the center of the circle with respect to the car.

A cargo plane is delivering to a South Pole research station. Flying horizontally at a height of 80 m, the pilot releases a package (drops out of plane) when they are 200 m (horizontally) from the target. If the package lands on the target, how fast war the plane moving when the package was dropped?

Ignoring complications like air-drag, think about the main force(s) acting on the package as it falls.

There are two dimensions of motion with the package, horizontal (in direction plane was traveling) and vertical.

If there is a vertical force, it will have no impact on horizontal velocity.

Likewise, if there is a horizontal force, it has no impact on vertical velocity.

More generally, a given force has no impact on velocity in directions to which the force is perpendicular.

Gravitational force on the surface of the earth roughly provides a falling object with constant acceleration (neglecting air drag). From this knowledge, and knowing the initial velocity, and the initial position of the package, you can calculate how long it will take to hit the ground.

In the same amount of time, it will travel some horizontal distance at the same horizontal speed it was moving before it was dropped (which is basically the same speed as the plane).

If you know the distance the package needs to travel horizontally, and the time it takes to travel that distance, then you can calculate the horizontal speed of the package (which we assume is constant) and this should equal the speed the plane was traveling.

Edited by mmiguel1
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Thanks...I got most of that...

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Thanks...I got most of that...

Which ones are not part of the most? If you still want help that is.

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From this knowledge, and knowing the initial velocity, and the initial position of the package, you can calculate how long it will take to hit the ground.

I just realized this might be confusing.

I meant here by velocity and position: vertical velocity and vertical position.

This vertical velocity is distinct from the horizontal velocity (plane speed).

Typically in problems like this, you would assume the box is dropped with an initial vertical velocity of 0, rather than thrown downwards or upwards.

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