Kinematics +
Linear Momentum
Linear Momentum
A box with a mass of 2 kg accelerates in a straight line from 4 m/s to 8 m/s due to the application of a force whose duration is 0.5 s. Find the average strength of this force.
16 N
A person who weights 800 N steps onto a scale that is on the floor of an elevator car. If the elevator accelerates upward at a rate of 5 m/s2, what will the scale read?
1,200 N
An astronaut drops a rock from the top of a crater on the Moon. When the rock is halfway down to the bottom of the crater, its speed is what fraction of its final impact speed?
1/√ 2
The gravitational acceleration on the surface of a planet (of mass M) with uniform volume density is g. What is the gravitational acceleration at a point halfway to the center of the planet (i.e., at r = rplanet/2)?
g/2
A compact disc has a radius of 6 cm. If the disc rotates about its central axis at a constant angular speed of 5 rev/s, what is the total distance traveled by a point on the rim of the disc in 40 min?
4.5 km
An object's location, in meters, after t seconds have passed is given by the equation
x(t)=-3t3+t2+6t
What is the maximum velocity of the object?
6.11 m/s
A ball attached to a string of length r rotates in a vertical circle. When the string is parallel to the ground and the ball is moving upward, the ball's velocity is v. What is the rate of change in the ball's speed at this point?
-g
A 4 kg box is pulled up a ramp of angle θ=30 degrees and height=5 m at a constant velocity. How much work is done by the normal force?
0 J
A planet moves in an elliptical orbit around the sun. Which of the following statements is true?
I. The angular momentum of the planet around the sun is constant.
II. The speed of the planet is constant.
III. The total energy (potential plus kinetic) of the planet is constant.
I and III only
Imagine a truck driving on the XY plane in the +y-direction. If it is slowing down, in what direction is the angular acceleration of its wheels?
In the +x-direction
An object moving with constant acceleration can have how many of the following path types?
I. a linear path
II. a circular path
III. a parabolic path
IV. an elliptical path
V. a spiral path
Two (linear + parabolic)
A 60 cm rope is tied to the handle of a bucket which is then whirled in a vertical circle. The mass of the bucket is 3 kg. What is the critical speed below which the rope would become slack when the bucket reaches the highest point in the circle?
2.4 m/s2
A uniform block of mass 10 kg is released at rest from the top of an incline of length 10 m and inclination 30◦. The coefficients of static and kinetic friction between the incline and the block are µs = 0.15 and µk = 0.1. The end of the incline is connected to a frictionless horizontal surface. After a long time, how much energy is dissipated due to friction?
87 J
Which of the following conditions are necessary for an object to be in static equilibrium?
I. The vector sum of all torques on the object must equal zero.
II. The vector sum of all forces on the object must equal zero.
III. The sum of the object’s potential and kinetic energies must be zero.
I and II only
A wheel with radius R, mass M, and rotational inertia I rolls without slipping across the ground. If its translational kinetic energy is E, what is its rotational kinetic energy?
EI/MR2
A car of mass 1,000 kg collides head-on with a truck of mass 2,000 kg. Both vehicles are moving at a speed of 21 m/s, and the collision is perfectly inelastic. After the crash, the two vehicles skid to a halt. Assuming friction is the only force acting on the vehicles after the collision, how much work is done by friction after the crash?
-73,000 J
Force of 20 N is pulling on a 2.0 kg block, which is attached to a 1.0 kg block. The coefficient of friction is equal to 0.2, so you must account for friction when summing forces. Find the tension in the rope between the blocks and the acceleration of the system of the blocks.
FT = 6.7 N
a = 4.7 m/s2
On a certain planet, a ball is thrown upward with a kinetic energy of 100 J and an angle of elevation of 45°. If the ball has a kinetic energy of 75 J at a height of 10 m, what is the maximum height of its trajectory?
20 m
A mass m is resting on a horizontal frictionless surface attached to a spring of spring constant k. At time t = 0, the mass is given a sharp blow, causing it to move to the right with speed v. When is the next time the mass will have this speed?
t = π√(m/k)
An inclined ramp with height h has a block at the top. The block of mass m slides to the bottom without friction. A second ramp of the same angle and height H is constructed, and a solid cylinder also of mass m rolls down the ramp without slipping. If the cylinder and the block have equal amounts of kinetic energy upon reaching the bottoms of their respective ramps, what is the relationship between h and H?
h = 2/3 H
A mass is launched off a cliff of height h with an initial speed of v0 and an angle of elevation of θ above the horizontal. How long is the mass in the air?
t=[v0sinθ±√(v02sin2θ+2gh)]/g
An introductory physics student, elated by a first semester grade, celebrates by dropping a textbook from a balcony into a deep layer of soft snow which is 3.00 m below. Upon hitting the snow the book sinks a further 1.00 m into it before coming to a stop. The mass of the book is 5.0 kg. Assuming a constant retarding force, what is the force from the snow on the book?
200 N
A person is at rest in a canoe that is motionless in still water. If the person begins to move with speed vp relative to the water, what is the kinetic energy of the person-canoe system? (The mass of the person and the canoe are mp and mc, respectively.)
KE = 1/2mpvp2(1+mp/mc)
A mass m hanging on a spring oscillates vertically. If the equilibrium point of the oscillation is a distance d below the relaxed length of the spring and if the amplitude of the oscillation is A, what is the maximum kinetic energy of the oscillation?
1/2(mg/d)A2
A horizontal bug of mass m stands at rest on the edge of a horizontal disk of mass M, radius r, and rotational inertia 1/2Mr2 which is also at rest. At a certain time, the bug starts walking counterclockwise around the rim (when viewed from above), so that it moves with a speed v with respect to the ground. If the disk is free to rotate about its center, what is the resulting angular velocity of the disk (with respect to the ground)?
ω = 2mv/(Mr)