a student performing the centripetal force experiment added some mass to the 25.0g acceleration block. when he did the experiment, he found that the speed at which the accelerated block separate from the magnet was 102 m/s^2. The radius of the circular motion before breakaway was 9.00 cm and the magnetic force between the accelerated block and magnet was .750N. A) calculate the mass added to the accelerated block. B)suppose the radius of the circular motion before breakaway was decreased to 8.00 cm, and nothing else was changed. calculate the new breakaway speed
A) To calculate the mass added to the accelerated block, we can use the formula for centripetal force:
Centripetal force (F) = (mass (m) x velocity (v)^2) / radius (r)
We're given the centripetal force (F) as 0.750N, the velocity (v) as 102 m/s, and the radius (r) as 9.00 cm (which we'll convert to meters by dividing by 100).
Thus, the formula can be rearranged as:
F = (m x v^2) / r
Solving for mass (m), we have:
m = (F x r) / v^2
Plugging in the values, we have:
m = (0.750N x 0.09m) / (102m/s)^2
m = (0.0675N m) / 10404 m^2/s^2
m ≈ 6.491 x 10^-6 kg
Therefore, the mass added to the accelerated block is approximately 6.491 x 10^-6 kg.
B) To calculate the new breakaway speed when the radius is decreased to 8.00 cm, we can again use the formula for centripetal force:
F = (m x v^2) / r
This time, we need to solve for the new velocity (v). Rearranging the formula, we have:
v^2 = (F x r) / m
Plugging in the given values, we have:
v^2 = (0.750N x 0.08m) / (6.491 x 10^-6 kg)
v^2 ≈ 924.212 m^2/s^2
Taking the square root of both sides, we have:
v ≈ √924.212 m^2/s^2
v ≈ 30.398 m/s
Therefore, the new breakaway speed, when the radius is decreased to 8.00 cm, is approximately 30.398 m/s.