A problem about a moving nickel coin - help/advice

[archivlad]

Please, help me with this:

Homework Statement

A nickel coin with diameter 2 cm and thickness 2 mm starts to roll with no friction on a horizontal plane with spped 10 cm/s. At 55.2 cm from the beginning the plane is inclined up. For the coin to go up to height max= 0.5 mm, what should be the maximum angle of inclination ? The rotation frequency is 1/2pi (s^-1), and the friction force down the inclined region is constand with f = 7.5 mikro Newtons.

also, the nickle density is 8.9 g/cubic cm

Homework Equations

conservation of energy, Newton's laws, laws of mechanical motion

The Attempt at a Solution

I receive an angle of ~40 degree, but I think something's wrong. Thanks for the advice!

 

[tiny-tim]

Welcome to PF!

Hi archivlad! Welcome to PF!

(have a mu: µ and a pi: π )

A nickel coin with diameter 2 cm and thickness 2 mm starts to roll with no friction on a horizontal plane with spped 10 cm/s. At 55.2 cm from the beginning the plane is inclined up. For the coin to go up to height max= 0.5 mm, what should be the maximum angle of inclination ? The rotation frequency is 1/2pi (s^-1), and the friction force down the inclined region is constand with f = 7.5 mikro Newtons.

also, the nickle density is 8.9 g/cubic cm
…
conservation of energy, Newton's laws, laws of mechanical motion

Yup … conservation of energy is the way to go!

Show us what you tried, and where you're stuck, and then we'll know how to help.

 

[thomate1]

As a scientist, my first piece of advice would be to double check your calculations and make sure all units are consistent. It's important to be precise and accurate when solving problems in physics.

Next, I would suggest using the laws of mechanical motion, specifically the conservation of energy and Newton's laws, to analyze the situation. The coin's motion can be broken down into translational motion (linear movement) and rotational motion (spinning). The coin's translational kinetic energy will be converted into potential energy as it goes up the incline, while its rotational kinetic energy will remain constant.

To find the angle of inclination, you can use the conservation of energy equation: mgh = 1/2mv^2 + 1/2Iω^2, where m is the mass of the coin, g is the acceleration due to gravity, h is the height it needs to reach, v is the coin's speed, I is the moment of inertia of the coin, and ω is the angular velocity.

You can also use Newton's second law, F=ma, to find the net force acting on the coin as it goes up the incline. The friction force and the component of the coin's weight parallel to the incline will act in the opposite direction of the coin's motion, while the normal force will act perpendicular to the incline.

By setting up equations and solving for the unknown angle, you can determine the maximum angle of inclination needed for the coin to reach the desired height. Remember to take into account the density of the nickel coin and its dimensions to find its mass and moment of inertia.

In conclusion, it's important to approach the problem systematically and use the appropriate equations to find the solution. If you're still unsure about your answer, you can always ask a classmate or your instructor for help. Good luck with your problem!