How Do You Calculate Forces in Circular Motion and Friction for Moving Objects?

[tjohn101]

Homework Statement

1) Estimate the force a person must exert on a string attached to a 0.100 kg ball to make the ball revolve in a circle when the length of the string is 0.600 m. The ball makes 1.00 revolutions per second. Do not ignore the weight of the ball. In particular, find the magnitude of FT, and the angle ϕ it makes with the horizontal. [Hint: Set the horizontal component of FT equal to maR; also, since there is no vertical motion, what can you say about the vertical component of FT?]

FT= N
ϕ= °

2) A car at the Indianapolis-500 accelerates uniformly from the pit area, going from rest to 285 km/h in a semicircular arc with a radius of 194 m.

Determine the tangential acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration.
m/s2

Determine the radial acceleration of the car at this time.
m/s2

If the curve were flat, what would the coefficient of static friction have to be between the tires and the roadbed to provide this acceleration with no slipping or skidding?

3) DONE

Homework Equations

1) unsure.
2) unsure.
3) DONE

The Attempt at a Solution

1) for FT, used FT=m*(v^2/r), but was unsure of what to use for r. It also says to not ignore the weight, but what do I do with it?

2) I don't even know where to start.

3) DONEI've been trying at these three for almost 3 days now. I have looked through the book and researched, but with no luck. Any help is greatly appreciated. Thank you!

 

[Redbelly98]

The Attempt at a Solution

1) for FT, used FT=m*(v^2/r), but was unsure of what to use for r. It also says to not ignore the weight, but what do I do with it?

Reread the hint. The horizontal component of FT is mv²/r. FT itself is not a horizontal force, but acts at some angle.

 

[tomcue]

Hello there,

I understand that you are having difficulty solving these homework problems and have been struggling for a few days. I can offer some guidance and tips to help you with these equations.

For the first problem, it is important to understand that the ball is undergoing circular motion, so the force that is causing it to revolve is the centripetal force. This force is given by the equation FT = m*v^2/r, where m is the mass of the ball, v is the velocity, and r is the radius of the circle. In this case, the radius is given as the length of the string, which is 0.600 m. So, you can calculate the centripetal force needed to make the ball revolve at 1.00 revolution per second.

However, the problem also mentions that you should not ignore the weight of the ball. This means that the weight of the ball must also be taken into account in calculating the force needed. Remember that weight is given by the equation W = mg, where m is the mass of the ball and g is the acceleration due to gravity (9.8 m/s^2). You can then find the angle ϕ by using the horizontal and vertical components of the force FT. The horizontal component will be equal to maR, where a is the tangential acceleration (since there is no vertical motion). The vertical component will be equal to the weight of the ball, which is mg. You can then use trigonometry to find the angle ϕ.

For the second problem, it is helpful to draw a diagram to represent the situation. The car is undergoing circular motion, so the same equations for centripetal force and acceleration apply. The tangential acceleration can be found by using the equation a = v^2/r, where v is the tangential velocity and r is the radius of the circle. Since the car is accelerating uniformly, the tangential acceleration will be constant throughout the turn. To find the radial acceleration, you can use the equation a = v^2/r, where v is the tangential velocity and r is the radius of the circle. The coefficient of static friction can then be found by using the equation μ = a/g, where μ is the coefficient of static friction, a is the radial acceleration, and g is the acceleration due to gravity.

I hope these tips and explanations will help you in solving these equations. Remember to always draw a diagram