At my local shopping center, I notice that all models of countertop blenders, even the most expensive ($500 USD), have plastic jars. I am concerned that if the blade inside comes loose or breaks while the power is on, that the blade will break through the glass. Are plastic blenders dangerous to use? Which material (e.g. glass, plexiglass) should I look for when choosing a model that will be used to blend fruits, meat, and vegetables?
Looking at it from a materials-science standpoint rather than a physics standpoint, I agree that plastic is safer than glass.
The difference is in how they break. Glass is stronger than plastic, for any plastic that a blender jar is likely to be made out of, and is less likely to break from, for example, trying to blend a spoon you forgot to remove. However, glass is also brittle.
When a plastic jar breaks, the most likely break is a single crack running up one side. The rest of the jar will flex to absorb the energy of the break and then return to its original shape. The jar will remain in one piece, without exposing any sharp edges.
When a glass jar breaks, it can't flex the way plastic can. Instead, the jar will shatter into two or more pieces, and unless it was made from tempered glass (unlikely) or laminated glass (even more unlikely), those pieces will be sharp-edged, making for a dangerous mess to clean up.
TL;DR: Plastic is better than Glass. It won't break (don't sue me if it does). If it does, you have about 0.0000518 seconds to get out of the way.
It has a powerful 750W motor.
A different blender that I saw with 35,000 rpm had a 1725W motor. This divides down to be ≈ 15,200 RPM.
The size: 40H x 18W x 18D
So the main box that the blade is in has size of 17W x 17H. The blade won't quite touch the edges, so let's say the diameter is 16cm. The circumference is therefore 16*3.14 ≈ 50.25
15,200 RPM means the tips are going 50.25 * 15,200 per minute, or ≈ 12,730 cm/s = 127.3 m/s The inner part of the blade will be going at ≈ 2,355 cm/s = 23.55 m/s (assuming a 6cm diameter hub).
The average of those two is ≈ 75.43 m/s. So let's say this sharpened stainless steel blade is going at 75 m/s when it breaks off.
If the blade is about 10g (12 - 13cm) then it has a force of about 5N per m2.
But this blade will hit a point ~ 1mm2, which is a force of 52,300,000N on that mm2 area. 523,000 = 523,000 pascals.
The force needed to break through glass is 33,000,000 pascals. The blade will not through. Acrylic, however, can be 2 or 3 times stronger. Therefore, a plastic blender may be better than a glass one, in terms of safety.
However, this was a 750W blender, if it was a 1500W blender, it could be up to 1,046,000 pascals hitting a piece of acrylic rated at 99,000,000 pascals. Stil not enough to get through. Enough to do some damage.
Important point: The blade won't break off. The implications of this are so severe, a blender is tested thoroughly before going onto the market. The biggest danger is finger slicing, not blade releasing.