Discussion:
Q1. Water drops are falling from the roof of the building 16 m tall through equal time intervals. When the first drop reaches the ground, the fifth one is leaving the roof. Find the distance between all drops at the time of first drop landing.
Q2. Prove, that if the object is thrown vertically up with velocity v0 it will land with same velocity. Show also that time of rising will be equal to the time of falling.
Q3. An object is dropped freely from the window of railway car. What will be the time of this object free fall if the car is: a) not moving; b) moving with constant velocity v; c) moving with acceleration a?
Q4. A fire hose held near the ground shoots water. At what angle should the nozzle point in order that the altitude of the water is equal to the distance of its landing?
Q5. What horizontal velocity has to be applied to an object to make if capable of traveling along equator line? Neglect any friction. Radius of Earth is 6400 km; g = 9.8 m/s2
Q6. A block of mass m1 lying on an inclined plane is connected to a mass m2 by a mass-less cord passing over a frictionless and mass-less pulley. Determine a formula for the acceleration of the system in terms of m1, m2, θ, and k, which is friction coefficient between a plane and mass m1. What conditions apply to masses for the acceleration to be in one direction? Neglect air resistance for mass m2.
Q7. A block of mass m is connected to an empty bucket of mass mb by a cord running over a frictionless pulley of mass mp and radius r. The coefficient of static friction between the table and the block is k. Sand is gradually added to the bucket until the system just begins to move. Derive the expression for the mass of sand ?m added to the bucket as well as the acceleration a of the system.
Q8. A small block of mass m is given an initial speed v0 up a ramp inclined at angle θ to the horizontal. It travels a distance d up the ramp and comes to rest. Derive the expressions for the coefficient of kinetic and static friction.
Q9. Two equal weights of mass M each are connected by a cord passing over a frictionless pulley of mass mp. and radius r. An additional weight of mass m is placed on one of the weights of mass M. Derive the expression for: a) system acceleration a; b) cord tension; c) forces on the pulley's axis; d) reaction between m and M; e) acceleration of the system's center of masses.