Kinematics
In a vacuum chamber, where air resistance is negligible, 1 kg of feathers and 1 kg of bricks are dropped at the same time. Which will reach the ground first?
They will reach the ground at the same time.
A box is compressed against a horizontal spring. When released, the box travels up a ramp and launches into the air. Draw a freebody diagram or the box when it is at its maximum height. Air resistance is negligible.
Fg down
A box is compressed against a horizontal spring. When released, the box travels up a ramp and launches into the air. How would a stiffer spring affect the maximum height the block reaches?
Increase in k, increase in Us
A person applies an impulse of 5.0 kg∙m/s to a box in order to set it in motion. If the person is in contact with the box for 0.25 s, what is the average force exerted by the person on the box?
20 N
A wheel is rolling, without slipping, up a ramp. Which direction is the frictional force acting on the wheel?
Down the ramp
On a velocity vs time graph, what feature would you look for in order to find a time when the object is at rest?
x-intercepts
A 50.0 N box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.50, and the coefficient of kinetic friction is 0.30. A horizontal 20.0 N force is then exerted on the box. What is the magnitude of the acceleration of the box?
0 m/s2
A cart with mass M is traveling along a horizontal surface in the positive direction. The cart then hits and sticks to a spring with spring constant, k, at time t1. Draw a graph of the position vs time graph for the resulting motion starting at time t=0 and ending after 2 oscillations.
t=0 to t1:increasing positive displacement
t1 on: oscillatory motion
A force of constant magnitude F and fixed direction acts on an object of mass m that is initially at rest. If the force acts for a time interval ∆t over a displacement ∆x , what is the magnitude of the resultant change in the linear momentum of the object?
F∆t
A child of mass M is on a circular platform of mass 2M that is rotating counterclockwe. Assume the platform rotates without friction. How could the child increase the angular speed of the child-platform system?
Move toward the center
A box is compressed against a horizontal spring. When released, the box travels up a ramp of angle theta and launches into the air. A graph of the horizontal displacement vs time is drawn to be a linear, positive slope. How would this graph change if the ramp had an angle greater than theta but less than 90?
The slope would be less but the graph would still be linear
A ball of mass M is attached to a string of length R and negligible mass. The ball moves in a vertical circle. Draw the FBDs for when the ball is at the lowest point on the circle and when the ball and string are perfectly parallel to the ground.
vertical: Fg down , FT up horizontal: Fg down , FT toward center
A block is compressed against a spring a distance -D from the natural length. When released and at the natural length (x=o), the block enters a surface with a coefficient of friction, mu, and slides a distance then comes to rest at a distance of 3D. If the spring were to be compressed twice as much, how far would the block slide then?
12D
A railroad car of mass m is moving with speed u when it collides with and connects to a second railroad car of mass 3m, initially at rest. How do the speed and kinetic energy of the connected cars compare to those of the single car of mass m before the collision?
Speed: Less
KE: Less
A massless rigid rod of length 3d is pivoted at a fixed point at 1d, and two forces each of magnitude F are applied vertically on the ends of the rod. A third vertical force of magnitude F may be applied, either upward or downward, at an increments of d. With the proper choice of direction at each point, the rod can be in equilibrium if the third force of magnitude F is applied at point.
1d from pivot point in either direction
A spring launcher with spring coefficient, k, is on a table top. When released, the spring launcher launches a block of mass m off a table with height h. Write an expression for the time it takes for the block to reach the ground in terms of k, m, h, and other physical constants
t = sqrt(2h/g)
A car is traveling along a road. The road has a hill that rises 8.0 m above the flat region. The top of the hill is a circular arc of radius 20 m. draw and label the forces (not components) that act on the car at the top of the hill if it travels over the hill without losing contact.
Fg down , Fn up
a system consisting of a block at the top of an inclined plane that rests on a table, which is located on Earth. The block and plane are at rest when the block is released. In trial 1 there is no friction between the block and the plane or between the plane and the table. In trial 2 the plane is fixed to the table so it cannot move, but there is still no friction between the block and the plane. In which trial will the block be moving the fastest relative to the table at the bottom of the ramp?
Trial 2
A small block of mass M is released from rest at the top of the curved frictionless ramp shown above. The block slides down the ramp and is moving with a speed 3.5v0 when it collides with a larger block of mass 1.5M at rest at the bottom of the incline. The larger block moves to the right at a speed 2v0 immediately after the collision. Express your answer in terms of the given quantities and fundamental constants. Was the collision elastic or inelastic?
Inelastic
A thin rod of length d and rotational inertia I on a frictionless surface is pivoted about one end and can rotate freely. The rod is at rest when it is struck by a sphere with mass m and linear velocity of magnitude v0 perpendicular to the rod. The sphere rebounds along its original line of motion with momentum of magnitude vbf . What is the magnitude of the angular velocity of the rod immediately after the collision?
w = md(v0 -vbf) / I
A track at angle theta to the horizontal has small speed bumps on it. The bumps are spaced a distance, d, apart. A cart of mass M is released from rest at the top of the track. A student notices that the average speed between bumps is not increasing and the from one bump to the next is constant. Sketch a velocity vs time graph that includes 4 bumps.
Sharp decrease over bumps Gradual increase between bumps So that the max and min v is the same for each bump.
The road a car is traveling along has a hill that rises 8.0 m above the flat region. The top of the hill is a circular arc of radius 20 m. You need to determine whether a car traveling under certain conditions will lose contact with the road at the top of the hill. There is a stop sign 50 m from the beginning of the hill. You are to assume that a car of mass 1600 kg accelerates uniformly from rest at the stop sign, has a speed of when it reaches the beginning of the hill, and then coasts with the engine off. Assume energy losses due to friction and air resistance are negligible. Calculate the minimum speed the car must have at the top of the hill to momentarily lose contact with the road.
14 m/s
A small block of mass M is released from rest at the top of the curved frictionless ramp shown above. The block slides down the ramp and is moving with a speed 3.5v0 when it collides with a larger block of mass 1.5M at rest at the bottom of the incline. The larger block moves to the right at a speed 2v0 immediately after the collision. Express your answer in terms of the given quantities and fundamental constants. Determine the height, h, of the ramp from which the small block was released.
6.12(v0 2/g)
A track consists of a frictionless arc XY, which is a quarter-circle of radius R, and a rough horizontal section YZ. Block A of mass M is released from rest at point X, slides down the curved section of the track, and collides instantaneously and in elastically with identical block B at point Y. The two blocks move together to the right, sliding past point P, which is a distance L from point Y. The coefficient of kinetic friction between the blocks and the horizontal part of the track is μ. Express your answer in terms of M, L, μ, R, and g. Determine the amount of kinetic energy lost due to the collision.
Klost = MgR/2
A wheel of radius R and negligible mass is mounted on a horizontal frictionless axle so that the wheel is in a vertical plane. Three small objects having masses m, M, and 2M, respectively, are mounted on the rim of the wheel. Mass M is 60 degrees above the horizontal, 2M is along the horizontal to the right and mass m is along the horizontal to the left. All masses are on the outside of the wheel. If the system is in static equilibrium, what is the value of m in terms of M ?
3M/2