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An object of mass 2 kg is travelling horizontally in a straight line at a constant velocity of magnitude 2 ms−1. The object is hit in such a way that it deflects 30° from its original path, continuing at the same speed in a straight line.
The magnitude, correct to two decimal places, of the change of momentum, in kg ms−1, of the object is
`E`
`text(Assume initial direction is along the)\ underset~i\ text(axis:)`
`underset~(p_1) = 2 xx 2underset~i = 4underset~i`
| `underset~(p_2)` | `= 2 xx (2cos30^@underset~i + 2sin30^@underset~j)` |
| `= 2sqrt3underset~i + 2underset~j` |
`underset~(p_2) – underset~(p_1) = (2sqrt3 – 4)underset~i + 2underset~j`
| `|underset~(p_2) – underset~(p_1)|` | `= sqrt((2sqrt3 – 4)^2 + 4)` |
| `~~ 2.07` |
`=>\ E`
A body of mass 3 kg is moving to the left in a straight line at 2 `text(ms)^(-1)`. It experiences a force for a period of time, after which it is then moving to the right at 2 `text(ms)^(-1)`.
The change in momentum of the particle, in kg `text(ms)^(-1)`, in the direction of the final motion is
A. − 6
B. 0
C. 4
D. 6
E. 12
`E`
| `m_1 v_1` | `= 3 xx -2 = -6` |
| `m_2 v_2` | `= 3 xx 2 = 6` |
| `Deltap` | `=m_2 v_2 – m_1 v_1` |
| `= 6 – (-6)` | |
| `= 12` |
`=> E`
A body of mass 2 kg is moving in a straight line with constant velocity when an external force of `8 N` is applied in the direction of motion for `t` seconds.
If the body experiences a change in momentum of 40 kg ms¯¹, then `t` is
A. 3
B. 4
C. 5
D. 6
E. 7
`C`
`sum F = 8 = 2a\ \ =>\ \ a = 4`
| `m(v – u)` | `= 40` |
| `2(v – u)` | `= 40` |
| `v – u` | `= 20` |
| `v` | `= u + at` |
| `v – u` | `= at` |
| `20` | `= 4t` |
| `:. t` | `= 5` |
`=> C`