Kinematics
I have a 1000 kg car that starts at rest and accelerates at 2 m/s2. How far does it go in 5 seconds?
xf=xi+vit+1/2at2
xf=0m+0m/s(5s)+1/2(2m/s2)(5s)2
xf=25 m
If I push a car with a mass of 200 kg with a force of 250 N and my friends push a bus with a mass of 600 kg with a force of 400 N, which vehicle is accelerating faster?
The car will accelerate more quickly.
a=F/m
acar=250 N / 200 kg=1.25 m/s2
abus=400 N / 600 kg=0.67 m/s2
If a bird is in the air and it's just hovering, does it have more potential energy or kinetic energy?
It has more potential energy (it has no kinetic energy if it's not moving).
If a bicycle and a train are moving at the same speed, which one has more momentum? Why?
The train because it has a bigger mass. (p=mv)
If I shoot a cannon perfectly horizontally off a cliff and at the same exact time I drop a ball from the cliff, which will land on the ground first?
They will both hit the ground at the same time (the horizontal and vertical motions are not affected by the other)
If I drop a ball off a cliff and it takes 4 seconds for it to hit the ground, how tall is the cliff?
xf=xi+vit+1/2at2
xf=0m+0m/s(4s)+1/2(10m/s2)(4s)2
xf=80m
Will it take more force to open a door by pushing on end or by pushing toward the hinge? How come?
It'll take more force to open it by pushing towards the hinge because the lever arm is shorter in this instance.
t=FL (to get the same torque, a shorter lever arm means a higher necessary force)
As a skier slides down a mountain, what happens to his potential energy? What happens to his kinetic energy?
His potential energy will go down (his height above the ground is decreasing and his kinetic energy will go up (his speed is increasing)
If the momentum of a car (m=1000 kg) is 20,000 kg*m/s, how fast is the car moving?
p=mv
20,000 kgm/s=1,000kg*v
v=20 m/s
Do we need friction in order to move?
Yes, it keeps us from sliding around everywhere.
If I am travelling at 20 m/s, not accelerating, how far will I travel in 5 s?
xf=xi+vt
xf=0m+20m/s(5s)
xf=100 m
If something weighs 100 N on a different planet, where the acceleration due to gravity is only 5 m/s2, what is the object's mass?
w=mg
100 N=m(5m/s2)
m=20 kg
If a frictional force of 3 N acts against a jetski that is moving 30 meters, how much work did the friction do against the jetski?
W=Fd
W=-3N(30m)=-90 J
(The work is negative because the friction is working in opposite direction that the jetski is moving)
If a car (m=1000 kg, v=20 m/s) that is travelling to the right hits a truck (m=2000 kg, v=5 m/s) that is travelling to the left, which direction will the cars move together after collision?
To the right (car has greater initial momentum)
p=mv
Car: p=1000kg(20m/s)=20,000 kgm/s
Truck: p=2000kg(5m/s)=10,000 kgm/s
If the Earth exerts a force on you (gravity), Newton's third law states that you exert a force back on the Earth. Then why doesn't the Earth accelerate towards you when you jump in the air?
The Earth's mass is much greater.
F=ma. Even though the forces are the same, the Earth accelerates much less because its mass is so much greater.
If I start with a velocity of 10 m/s and reach a final velocity of 100 m/s in 9 s, what is my acceleration?
vf=vi+at
100 m/s=10m/s+a(9s)
90 m/s=a(9s)
a=10 m/s2
You and a friend are on a see-saw that is not moving. If you (mass=60 kg) are 2 m from the axis and your friend is 3 m from the axis, what is the mass of your friend?
Torques (t=FL) must equal each other because the seesaw is not moving which means there is no net torque.
FL=FL and the force is the weight (mg)
mgL=mgL
60kg*10m/s2*2m=m*10m/s2*3m
m=40 kg
If a ball (m=100 g) is thrown in the air to a height of 2 m, how much potential energy does it have when it reaches its highest point?
PE=mgh=0.1kg(10m/s2)(2m)=2 J
A blue air hockey puck that has a mass of 2 kg is at rest. It gets hit by a red air hockey puck that has a mass of 1 kg and is moving at a velocity of 5 m/s. If the two hockey pucks move together after colliding, what will be their final velocity?
First find the total momentum of the system before the collision because the total momentum after the collision will be the same.
pbefore=2kg(0m/s)+1kg(5m/s)=5 kgm/s (this is the total momentum)
pafter=5 kgm/s = mtotalv
5 kgm/s=3 kg*v
v=1.67 m/s
If the area of a pipe decreases, what happens to the pressure of the water moving through it?
If the area decreases, then the velocity increases. If the velocity increases, then the pressure decreases.
An object is thrown vertically up from the ground with a velocity of 30 m/s. When will it reach its highest point?
At its highest point, the ball will have a velocity of 0 m/s.
vf=vi+at (in this case the only acceleration is due to gravity so a=g)
0=30 m/s+(-10m/s2)t
t=3 s
If I push on a box with 10 N of force to the right, and my friend pushes on the box with 4 N of force to the left, the box moves to the right with an acceleration of 2 m/s2. What is the mass of the box?
Fnet=ma
10N-4N=m*2m/s2
6N=m*2m/s2
m=3 kg
A baseball with a mass of 0.5 kg is 50 meters in the air at its highest point (its velocity is 0m/s). When it falls back down, what is it's speed right before it hits the ground? (hint: think about all the potential energy at the top being converted into kinetic energy at the bottom)
PEtop=KEbottom
mgh=1/2mv2
gh=1/2v2
v=Square root (2gh)=Square root (2*10m/s2*50m)
v=31.6 m/s
Two comets (both with a mass of 2,000 kg) are moving toward one another. One is moving at 500 m/s and the velocity of the other is unknown. After collision, they have a collective velocity of 200 m/s. What was the initial velocity of the other comet?
pf=mtotalv=4,000 kg(200 m/s)=800,000 kgm/s=pi
800,000=MV-mv=2000(500)-2000v
(subtract the momentums because they were initially moving in opposite directions)
v=100 m/s
How deep do I have to dive to reach a bottom pressure of twice atmospheric (top) pressure? Density of water is 1000 kg/m3 and atmospheric pressure is 100,000 Pa.
Pb = Pt + ρgh
200,000 Pa = 100,000 Pa + 1000 kg/m3(10 m/s2)h
h=10 m