physics - help

Question

Q: what type of force is gravity? Q: Two marbles are rolling horizontally on a table. The red marble travels at 1.22 m/s, while the blue marble travels at 1.67 m/s. If both roll off the table at the exact same time, which marble will hit the ground first? Q:When working in one dimension, what is the difference between adding and subtracting vector quantities, as compared to scalar quantities?

Answer 1

Hi Hannah,

 

To answer the first question, the marbles' velocity horizontally will not affect how quickly they drop. If they both roll off the table together, they will hit the ground at the same time. This is because their vertical motion is dictated by gravity, and it is separate from their horizontal motion.

 

If we assume that it takes exactly 1 second for the marbles to hit the floor after rolling off the edge of the table, they will have continued their horizontal motion, and assuming no friction, etc., the red marble will hit the ground 1.22 m away from the edge of the table, while the blue one will hit the ground 1.67 m away from the table.

 

In essence, you can split the motions, forces, etc., into orthogonal components and treat the separately.

 

 

The second question: In 1-D, there really isn't any practical difference between vector and scalar quantities. A vector has magnitude and orientation/direction, while a scalar has magnitude. In 1-D, you can argue that there is no direction possible, other than forward or backwards, and this is covered by whether the quantity is positive or negative. So the operations of addition and subtraction are the same for both vectors and scalars.

 

This assumes, of course, that the area of interest is only the 1-D space. A 1-D space embedded in a higher-dimensional space tends to attract attention with notions that you can locate things in the larger-dimensional space, but that is not working in the 1-D space. Simplest example would be the distance along a winding road: in 1-D, it's a simple scalar value, and that is enough to locate a point in the 1-D space. So it also acts as though it were a 1-D vector. However, embed that road in a 3-D space, and location is more complex; but it isn't 1-D.

 

For another example, to add vectors in 2-D (or higher-D) you resolve the vectors into orthogonal (1-D) components and add and subtract these components in each direction. You can add and subtract the vectors, or you can 'factor out' the unit vectors and add and subtract the scalar multiples. You get the same result.

 

Which brings us back to the first question, where we were able to deal with the marbles' falls in 1-D, and their horizontal motion in a different 1-D, all while using scalar quantities only to get the result.