Kinetic Friction and Hemispherical Dome

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SUMMARY

The discussion focuses on a physics problem involving a 2 kg block on a hemispherical dome with a radius of 10m. In Part 1, it is established that if the coefficient of kinetic friction (μk) is 0, the block will leave the dome at an angle θ of π/4 radians. In Part 2, with a kinetic friction coefficient of 0.3, the minimum initial velocity required for the block to leave the dome is calculated based on the forces acting on the block at the point of departure.

PREREQUISITES
  • Understanding of basic physics concepts such as forces and motion
  • Knowledge of kinetic friction and its effects on motion
  • Familiarity with trigonometric functions and angles in radians
  • Ability to apply Newton's laws of motion to solve problems
NEXT STEPS
  • Calculate the forces acting on the block at the point of leaving the dome
  • Explore the relationship between initial velocity and angle of departure
  • Investigate the effects of varying the coefficient of kinetic friction on motion
  • Study the dynamics of motion on curved surfaces in physics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators seeking to explain concepts related to friction and motion on curved surfaces.

engineer2b
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Homework Statement



There is a hemispherical dome that sits on a horizontal plane. It has a radius of 10m.
A 2 kg block sits on top of the dome.

Pt. 1: Assuming the coefficient of kinetic friction is 0, at what angle, θ, will it leave the dome?

Pt. 2: Assuming that μk is 0.3, what is the minimum initial velocity for which the block will leave the dome, and what angle will it leave?

Homework Equations


The Attempt at a Solution


When the block leaves the surface, there will cease to be any kinetic friction. It would seem as though the block would have to leave the dome at, or before pi/4; however, I could be incorrect in that inference.
 
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engineer2b said:

Homework Statement



There is a hemispherical dome that sits on a horizontal plane. It has a radius of 10m.
A 2 kg block sits on top of the dome.

Pt. 1: Assuming the coefficient of kinetic friction is 0, at what angle, θ, will it leave the dome?

Pt. 2: Assuming that μk is 0.3, what is the minimum initial velocity for which the block will leave the dome, and what angle will it leave?

Homework Equations





The Attempt at a Solution


You must show what you have tried so far. Hint: what is special about the forces at the instant when the block leaves the surface?
 

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