# Physics

posted by Lola

A boy is whirling around a stone tied at the end of a 0.71 m long string at constant angular speed of 4 revolutions per second in a plane perpendicular to the ground. The string breaks when it is making an angle of 54 degrees above the horizontal and the stone is on the way up. The stone is 0.93 m above the ground when this happens. How long does the stone take to hit the ground after the string breaks?

1. MathMate

"a stone tied at the end of a 0.71 m long string"
r=0.71 m

"4 revolutions per second"

Tangential speed, v0
=rω

"The stone is 0.93 m above the ground"
Distance above ground, h
= 0.93

"an angle of 54 degrees above the horizontal"
θ=54°

Vertical component of initial velocity, vv
=v0sinθ

Let t=time it takes to hit ground,
S=vv*t+(1/2)gt²
-0.93 = vv*t+(1/2)(-9.8)t²

Solve for t.
I get -0.051 sec. or 4 sec. approx.
We reject -0.051 because t>0.

2. Lilly

I tried doing the problem your way, but I got confused at the end.
For the equation S = w*t + (1/2)(-9.8)t**2, what was the value of w?
When I tried using w = v0 (17.844m/s), I got the same answers as yours
But when I tried using w = v0sin54 (14.4363m/s), I got different answers. I'm not sure which way is right. I'm leaning toward the latter one.

3. MathMate

You're quite right.
I have calculated for 5 revolutions per second. That is why they don't match your answers, which are on the right track.
I get now -0.06 and 3 seconds, and -0.06 is to be rejected.
Sorry for the inconvenience.

4. Lilly

Yes, I also got -0.06 and 3.00 seconds, so obviously the answer is 3.00 seconds.

5. MathMate

You're welcome!

## Similar Questions

1. ### Physics/Math

A certain string can withstand a maximum tension of 43 N without breaking. A child ties a 0.37 kg stone to one end and, holding the other end, whirls the stone in a vertical circle of radius 0.91 m, slowly increasing the speed until …
2. ### physics

A certain string can withstand a maximum tension of 40 N without breaking. A child ties a 0.37 kg stone to one end and, holding the other end, whirls the stone in a vertical circle of radius 0.91 m, slowly increasing the speed until …
3. ### PHYSICS

A boy is whirling around a stone tied at the end of a 0.55 m long string at constant angular speed of 5 revolutions per second in a plane perpendicular to the ground. The string breaks when it is making an angle of 53 degrees above …
4. ### p

A certain string can withstand a maximum tension of 41 N without breaking. A child ties a 0.35 kg stone to one end and, holding the other end, whirls the stone in a vertical circle of radius 0.91 m, slowly increasing the speed until …
5. ### physics

A stone tied to the end of a string, 80 cm long, is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 seconds what is the magnitude and direction of the acceleration of the stone?
6. ### physics

a stone is tied to the end of a string and is swung with a constant speed around a horizontal circle with a radius of 1.5m. if it makes two complete revolutions each second, what is the magnitude of its acceleration?
7. ### physics

A mass 5kg is whirled in a horizontal circle @ 1 end of a string 50cm long,the other end being fixed. If the string when hanging vertically will just support a load of 200kg mass without breaking,find the maximum whirling speed in …
8. ### PHYSICS

8) A rock of mass 400 g is tied to one end of a string that is 2.0 m in length and swung around in a horizontal circle. It takes 2 s to complete one circle. a. Find the angular velocity of the rock just as the string breaks. b. At …
9. ### physics

a .150kg object tied to a string is whirled in a horizontal circle ata constant angular speed of 3.50 revolutions per second. the tension is the string is 75newtons. what is the length of the string?
10. ### science

a stone weighing 0.2kg tied to the end of the string 0.6m long whorld in a horizontal circle in a speed of 150 revolutions per minute. calculte the tension and string

More Similar Questions