Solve Physics Problem: 500g Rock on 1m String Tilt Down at 10 Degrees

[rooster_17]

This might be an easy problem, but I am missing something and am not sure where to start so here is the problem:

A student ties a 500g rock to a 1.0-m-long string and swings it around her head in a horizontal circle. At what angular velocity, does the string tilt down at a 10 degree angle?

If anyone can help me get going on this problem I would greatly appreciate it.

 

[Galileo]

Draw a diagram and consider gravity and the centrifugal 'force' on the rock.
The net force must make a 10 degree angle with the horizontal.

 

[wais]

To solve this physics problem, we can use the equation for centripetal force, Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the rock, v is the velocity, and r is the radius of the circle (in this case, the length of the string). We also know that the force of gravity, Fg, is acting on the rock, causing it to tilt downwards.

To find the angular velocity, we can use the equation ω = v/r, where ω is the angular velocity, v is the linear velocity (which we can find using the given angle and radius), and r is the radius.

First, let's find the linear velocity. We can use trigonometry to find the horizontal and vertical components of the velocity. The horizontal component will be the same as the linear velocity, while the vertical component will be the velocity caused by the tilt of the string.

Using the given angle of 10 degrees, we can find the vertical component of the velocity using the equation v = gtanθ, where g is the acceleration due to gravity (9.8 m/s^2) and θ is the angle. Plugging in the values, we get v = 9.8m/s^2 * tan(10 degrees) = 1.70 m/s.

To find the horizontal component, we can use the Pythagorean theorem, v^2 = vhorizontal^2 + vvertical^2. Plugging in the values, we get vhorizontal = √(v^2 - vvertical^2) = √(1.70^2 - 1.70^2) = 0 m/s.

Now, we can use the equation ω = v/r to find the angular velocity. Plugging in the values, we get ω = 0 m/s / 1.0 m = 0 rad/s.

In conclusion, the angular velocity at which the string will tilt down at a 10 degree angle is 0 rad/s. This means that the rock will not tilt down at all, as the horizontal component of the velocity is 0 m/s. I hope this helps you understand and solve the problem.