d) Now what is the maximum speed the rock can have before the string breaks?A 68
ID: 1544544 • Letter: D
Question
d) Now what is the maximum speed the rock can have before the string breaks?A 680 g rock is whirled on the end of a string 45 cm long which will break under a tension of 25 N.
a) What is the highest speed the rock can reach before the string breaks? (Neglect gravity.)
b) If two other strings identical to the first were attached to the rock, how fast could the rock be whirled before the three strings would break?
Next the rock is held by two of the same 45 cm strings with ends 64 cm apart and whirled in a circle between them. Neglect gravity.
c) What is the radius of the circle of motion?
d) Now what is the maximum speed the rock can have before the string breaks?
Explanation / Answer
Accordring to the give problem,
A 680 gm rock is whirled on the end of a string 45 cm long which will break under a tension of 25 N.
There are 2 forces on the rock as it moves around the vertical circle. The direction of its weight is always down. The direction of the tension is always toward the center of the circle. The maximum velocity occurs when the rock is at the bottom of the circle. At this position, the tension force is directed up.
The centripetal force is the net vertical force = Tension – Weight
Fc = m v2/r
Net vertical force = T – m * g
m * v2/ r = T – m * g
v2 = (T – m * g) (r /m)
Maximum velocity = [(T – m * g) * (r ÷ m)]^0.5
Maximum velocity = [(25 – 0.680 * 9.8) * (0.45 ÷ 0.680)]0.5
Maximum velocity = [(18.336) * (0.45 ÷ 0.680)]0.5
Maximum velocity = 3.48 m/s
2)If two other strings identical to the first were attached to the rock, how fast could the rock be whirled before the three strings would break?
Now the maximum tension is 90 N
Maximum velocity = [(75 – 0.680 * 9.8) * (0.45 ÷ 0.680)]0.5
Maximum velocity = [(68.336) * (0.45 ÷ 0.680)]0.5
Maximum velocity = 6.72 m/s
3)Next the rock is held by two of the same 48 cm strings with ends 70 cm apart and whirled in a circle between them. Neglect gravity.
What is the radius of the circle of motion?
The two 45 cm long strings form 2 sides of an isosceles triangle. The base of the triangle is 70 cm. The radius of the circle is the altitude of the isosceles triangle.
According to the website above, altitude = [(L2 – (B/2)]0.5
L = 0.45 m, B = 0.64 m
Altitude = (0.452 – 0.322)0.5 = 0.3164 m
This is the radius of the circle.
4)Now what is the maximum speed the rock can have before the string breaks?
Use the same equation as above, but change the radius from 0.48 m to 0.3265 m
Maximum velocity = [(75 – 0.680 * 9.8) * (0.3164 ÷ 0.680)]0.5
Maximum velocity = [(68.336) * (0.3164 ÷ 0.680)]0.5
Maximum velocity = 5.64 m/s
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