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 need to use the centripetal force equation. The centripetal force is provided by the magnetic force between the accelerated block and the magnet.
The formula for centripetal force is:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the accelerated block
v is the speed of the accelerated block
r is the radius of the circular motion
To find the mass added, we need to rearrange the equation to solve for m:
m = (F * r) / v^2
Substituting the given values:
F = 0.750 N
r = 9.00 cm = 0.09 m
v = 102 m/s
m = (0.750 * 0.09) / (102^2)
m = 0.00675 / 10404
m = 6.498 × 10^-7 kg
Therefore, the mass added to the accelerated block is approximately 6.498 × 10^-7 kg.
B) To calculate the new breakaway speed when the radius is changed to 8.00 cm, we can use the same centripetal force equation as before.
Using the rearranged equation:
v = √(F * r / m)
Substituting the given values:
F = 0.750 N
r = 8.00 cm = 0.08 m
m = mass added, which we found in part A as 6.498 × 10^-7 kg
v = √(0.750 * 0.08 / 6.498 × 10^-7)
v = √(0.060 / 6.498 × 10^-7)
v = √9.24 × 10^4
v ≈ 303 m/s
Therefore, the new breakaway speed when the radius is decreased to 8.00 cm would be approximately 303 m/s.