Help with these HW problems involving grav acceleration, circular motion, etc?

[tjohn101]

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= 2.368705056(Your answer is incorrect.) N [Why is that not right? I feel as if I've forgotten something]
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.
Answer= m/s2
Determine the radial acceleration of the car at this time.
Answer= 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?
Answer= 3) What is the distance from the Earth's center to a point outside the Earth where the gravitational acceleration due to the Earth is 1/14 of its value at the Earth's surface?
Answer= m

4) What will a spring scale read for the weight of a 66 kg woman in an elevator that moves as follows?
A) upward with acceleration of 0.31g? [in Newtons]

B) downward with acceleration 0.31g? [in Newtons]I am NOT asking for you guys to do them for me. Instead, I would like it if you guys can help me get started by pointing out what steps I should use to get these done. Thank you.

 

[tjohn101]

I got that one. It was a problem with the picky rounding the HW website has. I'm still lost on the others, though.

 

[tomcue]

I am happy to provide guidance on how to approach these problems involving gravitation and circular motion.

1) To solve this problem, you will need to use the equation for centripetal force, which is given by Fc = mv^2/r, where m is the mass of the object, v is its velocity, and r is the radius of the circular motion. In this case, the force exerted by the string (FT) is equal to the centripetal force. So, you can set FT = mv^2/r and solve for FT. Remember to include the weight of the ball (mg) in your calculations. To find the angle ϕ, you can use trigonometry and the fact that the vertical component of FT must be equal to mg (since there is no vertical motion).

2) For this problem, you will need to use the equations for tangential and radial acceleration in circular motion. The tangential acceleration (at) is given by at = v^2/r, where v is the tangential velocity and r is the radius of the circular motion. The radial acceleration (ar) is given by ar = v^2/r, where a is the angular velocity. Since the car is accelerating uniformly, the tangential acceleration will be constant. To find the tangential acceleration at the halfway point, you can use the fact that the car has reached half of its final velocity, and solve for v. Then, plug this value into the equation for at to find the tangential acceleration. To find the radial acceleration, you can use the equation for ar and the fact that the car is moving at a constant speed, so its angular velocity is also constant. Lastly, to find the coefficient of static friction, you can use the equation μs = ar/g, where μs is the coefficient of static friction, ar is the radial acceleration, and g is the acceleration due to gravity.

3) To solve this problem, you will need to use the equation for gravitational acceleration, which is given by g = GM/r^2, where G is the universal gravitational constant, M is the mass of the Earth, and r is the distance from the Earth's center. Since the gravitational acceleration at the Earth's surface is given, you can set it equal to 1/14 of the gravitational acceleration at the distance you are trying to find. Then, solve for r.

4) For this problem, you will need to