Centripetal Acceleration/Rotational Motion HW Problem

AI Thread Summary
A block on a smooth sphere of radius 1m slides down due to gravity until it leaves the surface. The equations used include mgcosθ + N = mv^2/R, with N set to zero, leading to v^2 = Rgcosθ. The work-energy theorem is applied, resulting in the equation Rgcosθ = 2gR(1-cosθ). Solving for cosθ gives 3cosθ = 2, leading to cosθ = 2/3. The final speed at which the block leaves the surface is calculated as approximately 2.556 m/s, with a note of uncertainty regarding the initial equation's formulation potentially affecting the result.
EndoBendo
Messages
11
Reaction score
0
A block sits at the top of a smooth sphere of radius 1m. Suddenly, under the
force of gravity, It begins to slide down the surface of the sphere until it leaves the
surface. At what speed does it leave the surface?

mgcosθ + N = mv^2/R
But N =0
v^2 = Rgcosθ
V^2 = gcosθ
speed = v = ( 9.8cosθ)^0.5
Now,
from work energy theorem,
0.5mv^2 - 0 = mgR(1-cosθ)
Rgcosθ = 2gR(1-cosθ)
cosθ = 2(1-cosθ)
3cosθ = 2
cosθ = 2/3
Now
SPeed = v = (9.8 x 2/3)^0.5 = 2.556 m/s

I am unsure if there's supposed to be a 1/2 in front of the mv^2/R on the first line of my work, which would change the final value to 6.32 m/s
 
Physics news on Phys.org
sorry i meant 3.62 for the new value lol
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top