AP Physics C: Mechanics
4.2 Change in Momentum and Impulse
Four different one-dimensional forces act on identical blocks, each initially at rest on a frictionless horizontal surface, over the time interval \(0 \le t \le T\).
The functional form of each force is given in the table, where \(F_0\) and \(T\) are positive constants.
Which of the following correctly ranks the magnitude of the impulse \(J\) delivered to each block by its respective force during the interval from \(t = 0\) to \(t = T\)?
The functional form of each force is given in the table, where \(F_0\) and \(T\) are positive constants.
| Force Profile | Functional Form |
|---|---|
| Profile 1 | \(F_1(t) = F_0 \sin\left(\dfrac{\pi t}{T}\right)\) |
| Profile 2 | \(F_2(t) = F_0 \left(\dfrac{t}{T}\right)\) |
| Profile 3 | \(F_3(t) = 4F_0 \left(\dfrac{t}{T}\right)\left(1 - \dfrac{t}{T}\right)\) |
| Profile 4 | \(F_4(t) = F_0 \left(\dfrac{t}{T}\right)^2\) |
Which of the following correctly ranks the magnitude of the impulse \(J\) delivered to each block by its respective force during the interval from \(t = 0\) to \(t = T\)?
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