Kinematics
What is the area under a velocity vs. time graph called?
Displacement
What is the equation that describes the acceleration of two unequal masses m and M hanging over a frictionless, massless pulley?
a = g(M–m)/(M+m)
What is the general definition of work that can be applied to ALL situations?
W = integral of force with respect to displacement (area under a force vs. displacement graph)
W = change in energy
The position of a 2-kg object is given by x(t)=t4+3t. What is the kinetic energy of the object at t=2s?
1225 J
On what day was the winter solstice this year?
December 21
An object starts from rest at t=0. The velocity is given by v(t)=2t+3t2. How far does the object travel in the first 5 seconds?
150 m
A 10-kg block sits on a horizontal surface. A string pulls up on the block with 48 N of tension. What is the normal force on the block from the surface?
50 N
A competitive high-jumper just clears the bar at a speed of 1.25 m/s and later lands on the mat below at a speed of 6.15 m/s. How high is the bar above the mat?
1.85 m
How much faster will a ball released from a height of 4H be moving when it hits the ground compared to a ball released from a height of H?
Twice as fast
(2v)
What does the word "hanukkah" literally mean?
Dedication
A football is kicked with an initial speed of 20m/s at an angle of 33o above the horizontal. How far in the horizontal direction has the ball traveled when it reaches its maximum height?
18.64 m
A block of mass m sits at rest on a rough ramp inclined at an angle (theta). Write an expression for the frictional force acting on the block in terms of m and (theta), and fundamental constants as needed.
Ff = (m)(g)sin(theta)
A mouse of mass 200g falls 100m down a vertical mine shaft and lands at the bottom with a speed of 8.0m/s. During its fall, how much work is done on the mouse by air resistance?
–189.6 J
When is Mrs. Heyneman's birthday?
October 19
What person selected December 25 as the date to celebrate the Feast of the Nativity (later named Christmas) in the 4th century?
The Pope
(Pope Julius II)
A ball is dropped from a height H. A second ball is thrown vertically upward from the ground with an initial velocity v0. Derive an expression for the time t that the balls pass each other.
t = H/v0
A block accelerates down a rough 25o incline at a rate of 1.5 m/s2. What is the coefficient of kinetic friction between the block and the incline?
0.297
A 5-kg mass is moving in one dimension with a velocity given by v(t)=0.5t2. A t=4s, what is the instantaneous power delivered by the net force?
160 W
A constant force does 12 J of work on a 8-kg particle to accelerate it from rest over a time of 5 seconds. What is the acceleration of the particle?
0.346 m/s2
In what decade did the first New Year's Eve ball drop at Times Square in New York City?
1900's
(1907)
A cyclist traveling southeast along a road at 15km/h feels a wind blowing from the southwest at 25km/h. To a stationary observer, what are the speed and direction of the wind?
29.15 km/hr, 14o north of east
A competitive speed skater crosses the finish line of a race at a speed of 15 m/s and then slows down by coasting on his skates. The velocity-dependent resistive force acting on the speed skater while he coasts is f=–kmv2, where k=0.1 (drag coefficient) and m is the skater’s mass. What is the speed of the skater after coasting for 2 seconds?
3.75 m/s
The single force acts on a 2-kg particle. The velocity of the particle is given by v(t)=0.5t3+10. How much work is done by the force over the first 1 s?
10.25 J
A 0.5-kg block is attached to the free end of a horizontal spring with a spring constant k=100N/m. The spring is compressed by a distance of 20cm and the block is held at rest. When the block is released, it travels across a horizontal frictionless surface before reaching the bottom of a ramp inclined at 30o. If the coefficient of kinetic friction between the block and the ramp is 0.30, how far along the incline will the block move?
0.537 m (53.7 cm)
According to PNC Bank's Christmas Price Index, buying all the gifts listed in the "12 Days of Christmas" song would cost approximately how much in 2024?
$49,263
($40,000-60,000 accepted)