A mass m = 77 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 19.9 m and finally a flat straight section at the same height as the center of the loop (19.9 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.) ) What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? m/s What height above the ground must the mass begin to make it around the loop-the-loop? m If the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? m/s If the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (19.9 m off the ground)? m/s Now a spring with spring constant k = 17500 N/m is used on the final flat surface to stop the mass. How far does the spring compress? m It turns out the engineers designing the loop-the-loop didn’t really know physics – when they made the ride, the first drop was only as high as the top of the loop-the-loop. To account for the mistake, they decided to give the mass an initial velocity right at the beginning How fast do they need to push the mass at the beginning (now at a height equal to the top of the loop-the-loop) to get the mass around the loop-the-loop without falling off the track? m/s
A mass m = 77 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 19.9 m and finally a flat straight section at the same height as the center of the loop (19.9 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.) ) What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? m/s What height above the ground must the mass begin to make it around the loop-the-loop? m If the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? m/s If the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (19.9 m off the ground)? m/s Now a spring with spring constant k = 17500 N/m is used on the final flat surface to stop the mass. How far does the spring compress? m It turns out the engineers designing the loop-the-loop didn’t really know physics – when they made the ride, the first drop was only as high as the top of the loop-the-loop. To account for the mistake, they decided to give the mass an initial velocity right at the beginning How fast do they need to push the mass at the beginning (now at a height equal to the top of the loop-the-loop) to get the mass around the loop-the-loop without falling off the track? m/s
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A mass m = 77 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 19.9 m and finally a flat straight section at the same height as the center of the loop (19.9 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.)
)
What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track?m/s
What height above the ground must the mass begin to make it around the loop-the-loop?
m
If the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop?
m/s
If the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (19.9 m off the ground)?
m/s
Now a spring with spring constant k = 17500 N/m is used on the final flat surface to stop the mass. How far does the spring compress?
m
It turns out the engineers designing the loop-the-loop didn’t really know physics – when they made the ride, the first drop was only as high as the top of the loop-the-loop. To account for the mistake, they decided to give the mass an initial velocity right at the beginning
How fast do they need to push the mass at the beginning (now at a height equal to the top of the loop-the-loop) to get the mass around the loop-the-loop without falling off the track?
How fast do they need to push the mass at the beginning (now at a height equal to the top of the loop-the-loop) to get the mass around the loop-the-loop without falling off the track?
m/s
Transcribed Image Text:The image illustrates a physics concept involving motion and forces, depicted through a diagram with a track and a block. Here's the description:
1. **Track Layout:**
- The track begins with a curved slope on the left side with a red block positioned at the top. The block is oriented to slide downwards, as indicated by a blue arrow pointing downward, demonstrating the direction of motion or force acting on the block due to gravity.
- In the center, there is a vertical loop, representing a circular path with radius \( R \). The loop is shown with a green line radiating from the center to the edge, indicating the radius.
- On the right side, the track rises to a horizontal finish. The vertical distance from the base of the track to the top of this final rise is also marked with \( R \), suggestive of a height equal to the radius of the loop.
2. **Key Concepts:**
- This diagram can be used to discuss principles like gravitational potential energy, kinetic energy, conservation of energy, and centripetal force as it relates to objects moving in a circular path.
- The loop in the middle can demonstrate the speed and forces needed to maintain motion through a loop-the-loop without losing contact with the track.
Overall, this diagram can serve as a basis for explaining dynamics in a physics context, particularly focusing on energy transformations and forces in roller coaster-style motions.
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