L1
An intercontinental ballistic missile is a projectile. True or False, and why?
False. It has a propelling force, whereas projectiles have gravitational force as their only force.
(Some definitions include air resistance as well.)
In circular motion:
Direction of centripetal force is ___.
BONUS: Direction of instantaneous velocity is ___.
Radially inwards (or synonym).
BONUS: Tangential (or synonym).
In circular motion, F_net must equal F_c.
Discuss with an example.
False, e.g. vertical circular motion, where F_g introduces tangential force.
A random git throws an egg horizontally outward from the top of Chatswood interchange, hitting a cog student after 2 seconds in the air.
The second thought the student had was "This egg hit me with ___ ms^-1 vertical velocity!!"
v = u + at
v_y = 0 - 9.8*2
v_y = 19.6 ms^-1 downwards
F_g = F_c = mv^2/r
F_g = 10^6 * 10^(3*2) / 10^6 = 10^6 N
A projectile's instantaneous velocity is always the same for a given height.
True or False, and why?
Speed is same, direction of velocity changes. Speed is same by GPE <--> KE = 1/2*m*v^2, where v is speed.
The optimal launch angle is always 45deg, assuming no air resistance. True or False?
False. 45 is only optimal when the ground is also flat. E.g. for initial height --> infinity, optimal angle --> 0.
On vehicles travelling slightly BELOW the design speed on asphalt banked tracks, friction will be [static/dynamic/none] and act [up/down/not act] the ramp.
Static (no skidding), up (compensating for force down ramp)
The sheriff shots warning shot which travels 1.96km vertically upwards before falling back down and hitting him on the head.
What was its final velocity?
v^2 = u^2 + 2as
v^2 = 0 + 19.6 * 1960 (on the way down)
v = 196 ms^1
A turtle is getting sucked into a whirlpool. By paddling with the current, it can undergo uniform circular motion at 5ms^-1, allowing it to accelerate radially inward at 25ms^-2.
What is the diameter of the whirlpool?
a_c = v^2/r
d = 2r = 2v^2 / a_c
d = 2 *25/25 = 2m
Describe how vertical and horizontal velocity vary over time, for a projectile.
Vertical velocity decreases linearly from the initial, passing 0 at the max height to reach a negative minimum at impact.
Horizontal velocity is constant at the initial.
Describe how a projectile's vertical and horizontal displacement changes over time, if thrown upwards off a cliff.
Horizontal displacement increases linearly from 0 to a final value at impact.
Explain how changing the width of the screwdriver handle, and length of the screwdriver shaft, affects its effectiveness.
Fatter handle = larger r (force arm in plane of rotation)
Longer shaft = no effect (length not in plane of rotation)
An Angry Fowl is performing a kamikaze attack via slingshot towards a Naughty Piggy, from the bottom of a ditch 5.1m under ground level. It strikes the swine 1s after launching at 20ms-1 North at 30deg above the horizontal.
Where was the Piggy struck down?
s_y = u_y*t + 1/2*at^2
s_y = 20sin30' - 4.9 = 5.1m
h_f = h_i + s_y
h_f = -5.1 + 5.1 = 0m (ground).
s_x = u_x*t
s_x = 20cos30' = 17m N
Therefore Piggy was 17m North of slingshot on ground level.
A poorly designed rollercoaster has the minimum required speed to stay in contact to the tracks of a 9.8m high loop de loop.
What is its speed at the top of the loop?
F_net = F_g + N
At top, N=0, therefore F_net = F_c = F_g
mv^2 /r = mg
v = sqrt(gr)
v = sqrt(9.8*9.8) = 9.8ms^-1
t_maxheight
u_y
v_y
h_max
(also instantaneous v_y and s_y for any t)
Black dragon Boothless is tied to a boulder by a rope, and uniformly flying in a horizontal circle around it.
Explain the relationship between his angular and instantaneous velocity, and how this links to tension force.
v = w*r
Inst. vel is proport. to ang. vel. (if r constant)
T = F_c = m*w^2*r = m*v^2 / r
Tension, which acts as the centripetal force here, increases proport. to square of both inst. and ang. vel. (if r, m constant)
For any two spinning gears in contact, torque is always conserved.
True or False, and why?
False.
It is force that is always conserved, and by Tau = F_perp*r, therefore Tau2/r2 = F_perp = Tau1/r1, therefore if r is different, so is torque.
Brozone from Mr. Incredulous stands over an icy ramp, over flat ground. It is angled 45deg up at the end, and is 9.8m high. After he slides down and out, how much air time does he get?
dE = 0, dU = dK
mg(h) = 1/2*mv^2 (u=0)
v = sqrt(2gh) = 9.8*sqrt(2)
v_y = 9.8
At landing, v_y = -u_y = -9.8 (flat ground)
v = u + at
-9.8 = 9.8 - 9.8t
t = 2s
Broker operates a wrecking ball to destroy the Betmobile, which is driving around a 45deg angled bank track spanning 1960m in diameter.
What is the minimum angular velocity Broker needs to wipe out Betman?
v = sqrt(gr*tanT)
v = sqrt(9.8*980*1)
v = 98ms^-1
w = v/r
w = 98/1960
w = 1/20 = 0.05 rad/s
i.e. need more than 0.05rad/s to work.
Name FIVE sets of TWO variables that together are enough to solve every other parameter of a projectile's motion. (e.g. v; theta landing)
Assume the ground is flat.
u, theta launch
h_max, t_flight
R, t_flight
u, t_flight
v,t_flight
etc. etc. etc.
Name FIVE sets of THREE variables that together are enough to solve every other parameter of a projectile's motion. (e.g. v; theta landing; h)
DO NOT assume the ground is flat.
u, theta launch, h
u, theta launch, t_flight
v, theta land, t_flight
h_max, t_flight, h
R, t_flight, h
u, t_flight, h
v, t_flight, h
etc. etc. etc.
Name TWO similarities and THREE DIFFERENCES between vertical and horizontal circular motion.
SIMILARITIES
1) Path is circle
2) F_c = mv^2/r works for each instant of time
DIFFERENCES
1) Gravity present, i.e. F_net =/= F_c
2) Tangential force in vert. --> tangential accel --> change of tangential velocity
3) Source of centrip. force e.g. tension will NOT be constant in vert.
In Revengers, Civil War, Billionaire playboy Bony Bark's bropulsar beam just intercepted Bawkeye's arrow 10 seconds after it was released, at 590m away and 100m below where it was shot from.
You, Barvis, tell Bony that its initial velocity was ___.
s_y = u_y*t + 1/2*at^2
u_y = s_y/t - 1/2*at
u_y = 100/10 + 4.9*10 = 59ms^-1
u_x = s_x/t
u_x = 590/10 = 59ms^-1
u = 59*sqrt(2) = 83m/s; 45deg above hori.
I'm pedalling to the station, exerting 600N force at 60deg from perpendicular to the 10cm pedal arm. The pedal is connected to a 20cm gear, which spins against a 10cm wheel gear connected to a 60cm wheel.
What is the torque experienced by the wheel?
F_pedalperp = F_pedal * cosT = 600*1/2 = 300N
Torque_pedalaxle = F_pedalperp * r = 300*0.1 = 30Nm
Torque_gear1 = Torque_pedalaxle = 30Nm (connected)
Torque_gear1/r1 = Torque_gear2/r2 (= force_perp)
Torque_gear2 = Torque_gear1*r2/r1
Torque_gear2 = 30*0.05/0.10 = 15Nm
Torque_wheel = Torque_gear2 = 15Nm (connected)