Top part: The question GIVES you the formula to use, and all the numbers to fill into the formula.
The tension in the string is the 'F' in the formula F = m v² / r .
The 'm' is the mass of the rock out at the end of the string, the 'v' is the speed of the rock as it's going around the circle at the end of the string, and the 'r' is the length of the string ... the radius of the circle.
This question GIVES you the 'm', the 'v', and the 'r', and it wants you to find the 'F'. All you have to do is write the numbers in place of the letters in the formula, and 'F' will practically calculate itself and jump up off the paper at you.
F = m v² / r
F = (1 kg) (4 mtr/s)² / (1 mtr)
F = (1 · 4² / 1) (kg · mtr²) / (s² · mtr)
F = 16 kg·mtr/s²
F = 16 Newtons
= = = = =
Bottom half, spinning another rock on the end of another string, 4 questions:
Same formula: F = m v² / r
The 'm' is the mass of the rock out at the end of the string, the 'v' is the speed of the rock as it's going around the circle at the end of the string, and the 'r' is the length of the string ... the radius of the circle. The 'F' in the formula is the tension in the string.
Before we start answering the questions, let's find the tension in the string NOW, before anything changes:
F = m v² / r
F = (2 kg) (3 mtr/s)² / (3 mtr)
F = (2 · 9 / 3) Newtons
F = 6 Newtons
Now, All of these 4 questions ask how the tension in the string would change if the mass, the speed, or the length changes. So there's one more thing to do before we jump into the questions: Look at the formula, and see what happens to F when m, v, or r changes.
F = m · v² / r
mass -- 'm' multiplies everything else on the right side of the formula, so if you multiply the mass by any number, then 'F' is multiplied by the same number.
speed (v) -- everything on the right side of the formula is multiplied by the square of v, so if we multiply v by any number, then F gets multiplied by the square of that number.
radius (length) -- The length of the string is in the denominator of the formula, so if we multiply r by any number, then F gets divided by that number.
Now we're ready to blast through the four questions (and then I guess we'll drink the wine):
a). Twice the mass ... That makes F twice as big, so the tension changes from 6N to 12N.
b). Twice the speed ... That makes F (2²) = 4 times as big, so the tension changes from 6N to 24N.
c). Twice the length of string (r) ... That divides F by 2, so it changes from 6N to 3N.
d). Change everything: Twice the mass --> Double F. Twice the speed --> 4 times F . Twice the length --> 1/2 F.
Puttum all together: (2) · (4) · (1/2) F . That's 4 x F . So the tension changes from 6N to 24N.
