Physics Work,Power & Energy Level: High School
(a) Three carts of masses 4.00 kg , 10.0 kg and 3.00 kg moves on a frictionless horizontal track with speeds of 5.00 m/s , 3.00m/s and 4.00 m/s as shown in the figure at “click here” . Velcro couplers make the carts stick together after colliding . Find the final velocity of train of three carts .(b) Does your answer require that all the carts collide and stick together at the same time ? What if they collide in a different order ?
Physics Work,Power & Energy Level: High School
High-speed stroboscopic photographs show that the head of a golf club of mass 200g is traveling at 55.0 m/s just before it strikes a 46.0 g golf ball at rest on a tee . After the collision , the club head travels (in the same direction) at 40.0 m/s . Find the speed of the golf ball just after impact .
Physics Work,Power & Energy Level: High School
A tennis player receives a shot with the ball (0.060 kg) traveling horizontally at 50.0 m/s and returns the shot with the ball traveling horizontally at 40.0 m/s in the opposite direction .(a) What is the impulse delivered to the ball by the racquet ?
(b) What work does the racquet do on the ball ?
Physics Rotational Mechanics Level: High School
A block of mass m slides at speed v on a frictionless surface and strikes a previously stationary block of mass 4m which is attained to a spring of constant k . After collision the first block bounces back to left at a speed v/3 . Find the maximum compression.
Physics Rotational Mechanics Level: High School
A particle of mass M is moving on a frictionless horizontal table and is attached to a massless string whose other end passes through a hole in the table where I am holding it . Initially particle is moving in a circular of radius r_0 with angular velocity w_0 but I now pull the string down through the hole until a length r remains between the hole and particle , What is the particle angular velocity now ?
Assume that I pull the string so slowly that we can approximate the particles path by a circle of slowly shrinking radius , calculate the work I did pulling the string and compare this answer with the particles gain in Kinetic energy ?
Physics Rotational Mechanics Level: High School
Calculate the x and y coordinates of the center of mass of the following object . Assume the object is of uniform mass density .
Physics Rotational Mechanics Level: High School
A tennis ball is a hollow sphere with a thin wall . It is set rolling without slipping at 4.03 m/s on a horizontal section of track , as shown in the figure at “click here”. It rolls around the inside of a vertical circular loop 90.0 cm in diameter and finally leaves the track at a point 20.0 cm below the horizontal section .(a) Find the speed of the ball at the top of the loop . Demonstrate that it will not fall from the track .
(b) Find its speed as it leaves the track .
(c) Suppose that static friction between the ball and track were negligible , so that the ball slid rather instead of rolling . Would its speed then be higher , lower , or same at the top of the loop ?
Physics Rotational Mechanics Level: High School
The top shown has a moment of inertia of 4.00 x 10^-4 kgm^2 and is initially at rest . It is free to rotate about the stationary axis AA’. A string wrapped around a peg along the axis of the top , is pulled in such a manner as to maintain a constant tension of 5.57 N , If the string does not slip while it is unwound from the peg , what is the angular speed of the top after 80.0 cm of string has been pulled off the peg ?
Physics Rotational Mechanics Level: High School
A block of mass m1 = 2.00 kg and a block of mass m2 = 6.00 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M= 10.0 kg . These blocks are allowed to move on a fixed block-wedge of angle theta = 30 degrees as shown at “click here” . The coefficient of kinetic friction is 0.36 for both blocks . Draw a free-body diagrams of both blocks , as well as the pulley . Determine(a) The acceleration of the two blocks.
(b) The tensions in the string on both sides of the pulley.
Physics Rotational Mechanics Level: High School
Many machine employ cams for various purposes , such as opening and closing valves . In this problem , our cam is a circular disc rotating on a shaft that does not pass through the center of the disk . In the manufacture of the cam, a uniform solid cylinder of radius R is first machined . Then an off-center hole of radius R/2 is drilled , parallel to the axis of the cylinder , and centered at a point a distance R/2 from the center of the cylinder . The cam of mass M , is then slipped onto a cylindrical shaft and welded into a place . What is the kinetic energy of the cam when it is rotating with angular speed w(omega) about the axis of the shaft ?
Physics Rotational Mechanics Level: High School
Calculate the moment of inertia of a thin plate, in the shape of a right triangle as shown in the figure at “click here” . Let M represents the mass of the triangle and L the length of the base of the triangle perpendicular to the axis of rotation . Let h represent the height of the triangle and w(omega) the thickness of the plate , much smaller than L or h. Use the integral form of the moment of inertia equation . Let an element of mass consist of a vertical ribbon within the triangle , of width dx , height y, and thickness w . With x representing the location of the ribbon, show that y = hx/L . Show that the density of material is given by p=2M/L wh . Show that the mass of the ribbon is dM = pywdx = 2Mxdx/L^2 . Then calculate the moment of inertia from the integral equation .
Physics Rotational Mechanics Level: High School
Rigid rods of negligible mass by lying along the y axis connect three particles as shown in the figure at “click here”. If the system rotates rotates about the x axis with an angular speed of 2.00 rad/s . finda. the moment of inertia about the x axis and the total kinetic energy evaluated from 1/2lw^2.(w=omega)
b. the tangential speed of each particle and the total kinetic energy evaluated from 1/2 mv^2
Physics Rotational Mechanics Level: High School
A car traveling on a flat ( unbanked ) circular track accelerates uniformly from rest with a tangential acceleration of 1.70 m/s^2 . The car makes it one quarter of the way around the circle before it skids off the track . Determine the coefficient of static friction between the car and track from these data .
Physics Rotational Mechanics Level: High School
A car accelerates uniformly from rest and reaches a speed of 22.0 m/s in 9.00s . if the diameter of the tire is 58.0 cm , find(a) The number of revolutions the tire makes during the motion , assuming that no slipping occurs .
(b) What is the final angular speed of a tire in revolutions per second ?
Physics Rotational Mechanics Level: High School
A rotating wheel requires 3.00 s to rotate through 37.0 revolutions . Its angular speed at the end of the 3.00 s interval is 98.0 rad/s . What is the constant angular acceleration of the wheel?