Flashcards · 8 cards

Momentum, projectiles, work & energy

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Know it
What is impulse?
Answer
$Ft = mv - mu$ : force × time = change in momentum.
From the lesson: Momentum, impulse and collisions
Rule
A ball hits a wall at $u$ and bounces back at $v$ . What is the change in its velocity?
Answer
$u + v$ , not $v - u$ . Take "away from the wall" as positive: it changes from $-u$ to $v$ .
Bouncing backAway from the wall positive: v − (−u) = u + v
From the lesson: Momentum, impulse and collisions
Know it
The principle of conservation of momentum?
Answer
In a collision, the total momentum before equals the total momentum after.
From the lesson: Momentum, impulse and collisions
Rule
Two bodies collide and move off together. The equation?
Answer
$m_1u_1 + m_2u_2 = (m_1 + m_2)v$ . A velocity in the opposite direction goes in as negative.
Two bodies joinm₁u₁ + m₂u₂ = (m₁ + m₂)v
From the lesson: Momentum, impulse and collisions
Rule
The position of a projectile, speed $u$ at angle $\theta$ , after time $t$ ?
Answer
$x = (u\cos\theta)t$ and $y = (u\sin\theta)t - \frac12gt^2$ .
The path of a projectilex = (u cos θ)t; y = (u sin θ)t − ½gt²
From the lesson: Projectiles
Know it
The time of flight, greatest height and range of a projectile?
Answer
$T = \dfrac{2u\sin\theta}{g}$ , $H = \dfrac{u^2\sin^2\theta}{2g}$ and $R = \dfrac{u^2\sin 2\theta}{g}$ .
From the lesson: Projectiles
Know it
At what angle is the range greatest for a given speed?
Answer
$45^\circ$ , where $\sin 2\theta = 1$ .
From the lesson: Projectiles
Which method?
WAEC 2018 · Paper 2 · Q8
A body of mass $20\text{ kg}$ moving with a velocity of $80\text{ m s}^{-1}$ collides with another body of mass $30\text{ kg}$ moving with a velocity of $50\text{ m s}^{-1}$ . If the two bodies moved together after collision, find their common velocity if they moved in the:
same direction before collision;
opposite directions before collision.
How do you handle "opposite directions" in (b)?
Answer
Make one direction positive and the other negative: $20(80) + 30(-50) = 50v$ .
From the lesson: Momentum, impulse and collisions Try the question