Could someone verify the answers. I don't know question C and D
Thank you!
1. In physics, the formula for centripetal force is F =
mv^2/
r
where m is the mass, v the velocity, and r the radius.
a) Find the length of a string when a mass of 2.4kg is being spun at a speed of 5 m/sec if the centripetal force
is 15.8 N. Round your answer to the nearest tenth.
Answer: 3.8m
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b) What length would the string need to be to increase the force to 20.5 N if the speed is 5 m/sec and the
mass is 2.4 kg?
Answer: 2.9m
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c) If the string is made longer, but the mass and velocity are kept the same, how will this effect the force?
d) What would be the effect on the centripetal force if the mass and velocity were kept the same and the
length of the string was doubled?
a and b are ok
since F varies directly with m and v^2, but inversely with r, increasing r decreases F, as you see if you compare the answers to a and b.
since F varies directly with m and v^2, but inversely with r, doubling r halves F.
To verify the answers for questions C and D, we need to understand the relationship between the different variables in the formula for centripetal force.
In the given formula: F = (mv^2) / r, where F is the centripetal force, m is the mass, v is the velocity, and r is the radius (length of the string).
C) If the string is made longer, but the mass and velocity are kept the same, how will this affect the force?
When the length of the string (r) is increased while keeping the mass and velocity constant, the centripetal force (F) will decrease. This is because in the formula, centripetal force is inversely proportional to the radius. As the radius increases, the force required to keep the object moving in a circular path decreases.
D) What would be the effect on the centripetal force if the mass and velocity were kept the same and the length of the string was doubled?
If the length of the string is doubled (2r), while keeping the mass and velocity constant, the centripetal force will also double. This is because in the formula, centripetal force is directly proportional to the square of velocity (v^2) and inversely proportional to the radius (r). When the radius is doubled, the denominator of the formula becomes 4 times larger, resulting in the force becoming 4 times smaller. Therefore, to maintain the same centripetal force, it needs to be doubled.
In summary:
C) Increasing the length of the string while keeping mass and velocity constant will decrease the centripetal force.
D) Doubling the length of the string while keeping mass and velocity constant will double the centripetal force.