Your glass half full travels across the table at initial speed vi = 2.6 m/sec. Glass and water together add up to a mass of m = 0.22 kg. The underside is wet, so kind of slippery, with frictional force f = 0.29 N retarding the motion.
So what is the question? The angle of the water surface from horizontal?
tan angle = .29 / (m g)
To determine the final speed (vf) of the glass, we can use the concept of Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. Mathematically, it can be represented as:
Fnet = m * a
where:
Fnet is the net force acting on the glass (in this case, due to friction),
m is the mass of the glass (including water), and
a is the acceleration of the glass.
In this case, the net force acting on the glass is the frictional force (f), which is retarding the motion. So we can rewrite the equation as:
f = m * a
Then, we can rearrange the equation and solve for the acceleration (a):
a = f / m
Substituting the given values: f = 0.29 N and m = 0.22 kg, we can calculate the acceleration:
a = 0.29 N / 0.22 kg
a ≈ 1.32 m/s²
Now, we need to determine the final speed of the glass (vf). We can use the concept of uniformly accelerated motion, which relates initial velocity (vi), final velocity (vf), acceleration (a), and displacement (d). The equation is as follows:
vf² = vi² + 2ad
Given that the glass is initially at rest (vi = 0 m/s), we can simplify the equation to:
vf² = 2ad
By substituting the known values: a = 1.32 m/s² and d (unknown), we can find the final velocity squared (vf²). Since d is not provided, we assume the displacement is the distance traveled by the glass while experiencing the frictional force.
Finally, to find vf, we take the square root of vf²:
vf = √(2ad)
Plug in the values of a and d, then calculate to determine the final speed of the glass.