Kinematics
Two cars are 100 meters apart at time t = 0 s. Car A is travelling to the right at a speed of 15 m/s. Car B is travelling to the left at a speed of 10 m/s. At what time do they crash into each other?
4 s
What is the normal force exerted on a 65kg person by an elevator that is accelerating upward at 2.6m/s2?
806 N
In a storage warehouse, a 400kg pallet of lumber is picked up from a 60m-high shelf, brought to the ground, and put back by a forklift. What is the total amount of work done by the forklift on the pallet of lumber? Give a brief explanation why.
0 J because the displacement of the pallet is 0m since it was put back after being lifted from the shelf.
A force of 150 N compresses a spring with a spring constant of 575 N/m. How much energy is stored in the spring?
19.565 J
u = -4 î - 5.3 ĵ
v = 1.2 î - 2 ĵ
w = -0.5u + 3v
What is the magnitude of w?
6.526
A cheetah, starting from rest, accelerates uniformly at 8 m/s2 for 3s and then continues running at constant speed for an additional 2.8s. How much ground does the cheetah cover during the entire 5.8 s?
103.2 m
What is the highest velocity at which a car can drive over the top of a hill of radius 120m without leaving the ground?
34.293 m/s
A box of mass 5.2 kg is being pulled horizontally by a force at an angle 27° above the horizontal. The vertical component of this force is 91 N. What distance does the block have to be pulled for the force to do 2500 J of work?
14 m
A block from rest is dropped directly downward from a height h and hits the ground with a final velocity v. To double the block's velocity upon landing, at what height should it be dropped from? Provide a brief, qualitative explanation.
4h
u = 12cos(45) î + 12sin(45) ĵ
v = 1.5cos(45) î + 0.75sin(45) ĵ
Find u ⋅ v
27
A stone is thrown at an angle of 35° above the horizontal with an initial speed of 6.3 m/s. What will be the speed of the stone 0.12s after it was thrown?
5.707 m/s
Newton's Law of Gravitation describes the forces exerted by objects on each other due to gravitational attraction. This will be briefly explained by Luis if necessary.
Using Newton's Law of Gravitation, show that acceleration due to gravity at Earth's surface is approximately 9.8 m/s2. The following constants may be useful:
G = 6.67*10-11 N*m2/kg2
ME = 5.97*1024 kg
RE = 6.371*106 m
answer
A 300-Watt electric wheelchair has a mass of 50kg, and is able to carry a 50kg occupant up a long ramp at a constant velocity. About how much time does it take the wheelchair to reach the top of a 10m high ramp?
32.67 s
A vertical cannon of length 10m is used to accelerate a 1.0kg ball straight up into the air. A constant force of 13.2 N is used to accelerate the bowling ball up the length of the cannon. What is the approximate velocity of the ball as it leaves the cannon assuming no loss of energy due to friction? (use Work-Energy)
8.246 m/s
A = 6 î - 4.3 ĵ
B = -7 î + 2 ĵ
C = 2A + 1.5B
What is the direction of C?
-75.0°
75.0° Clockwise
285° Counterclockwise
A projectile is launched from the ground at an angle θ and with an initial velocity v0. It lands at the same height it was launched at. Show that the horizontal distance (or the range) the projectile travels is given by:
R = v02sin(2θ)/g
answer
A truck of mass M = 1200kg is moving up a hill with a constant acceleration a. A block of mass m = 3.3kg is held in place by static friction, with coefficient of friction 0.56 between the block and truck bed. There is no friction between the truck and the incline. The hill is inclined at 22° with respect to the horizontal. What is the maximum acceleration the truck can have before the block will slip?
1.417 m/s2
At the top of a ledge of height h sits a block with mass m and a spring oriented horizontally. The spring has a spring constant k. If we were to use the spring to get the block across a gap of distance d at the bottom of the ledge, how much should the spring be compressed?
x = D sqrt(mg/2hk)
A bead starts at rest on a mostly frictionless track at a height h above the ground. The flat portion of the track has friction. It has a coefficient of friction uk and has a length L. There is a loop with radius R after the flat part of the track. Find a condition on uk such that the bead can still clear the loop.
uk < (h-2L)/R
A particle that starts from rest begins to move in a circle of radius 16m. Every second, its speed increases by 4 m/s. What is the angle between the particle's acceleration and velocity vectors?
45°
Jerk (j) is defined as the rate of change of acceleration. Suppose an object is travelling such that jerk is constant. Derive kinematic equations that describe its acceleration, velocity, and position as functions of time.
a = jt + a0
v = v0 + a0t + (1/2)jt2
x = x0 + v0t + (1/2)a0t2 + (1/6)jt3
A block is at rest at the top of a sphere of radius R. It is given a small nudge, causing the block to slide down the surface of the sphere. Relative to the vertical, at what angle does the block lose contact with the sphere?
48.19°
A block of mass m rests on a flat, frictionless table. A constant force pushes the block a distance d such that the block has some final velocity v. Prove that the work done by this force is equal to the block's kinetic energy.
W = Fd, and F=ma, therefore W=mad
v^2 = 2ad, therefore a = v^2/2d
W = m*(v^2/2d)*d
W = (1/2)mv^2
The Lagrangian (ℒ ) of a system is defined as its total kinetic energy subtracted by its total potential energy. Find the Lagrangian ℒ of the double pendulum system drawn by Luis.
ℒ = (1/2)m1(vx12+vy12) + (1/2)m2(vx22+vy22) + m1gl1cos(θ1)+m2g(l1cosθ1 + l2cosθ2)
HighTown airport lies 600km directly northeast of LowTown airport. An aircraft currently over LowTown airport ends up directly over HighTown airport 45 minutes later. Throughout the aircraft's journey, the wind was blowing due east at 40 km/hr relative to the ground. If the aircraft flew at a fixed altitude at a constant velocity relative to the ground, what was its speed relative to the air during its journey? (keep your answer in km/hr)
772.234 km/hr