Verify that your equation has the masses and the velocities before and after the collision. If not, review your result with a classmate or your instructor. Solve the equation for the initial velocity of the projectile, vo.
Note that to calculate the initial projectile velocity vo, the velocity V of the block and projectile combination needs to be known. (The values of the masses can be determined with a balance.) So far, only one conservation principle has been used—the conservation of linear momentum. Now consider the mechanical energy of the system after the collision. Write an expression for the kinetic energy of the system (the mass and bob combo) immediately after collision, and label it Eq. 2.
As the bob swings upward from h1 to a maximum height h2 (GL Fig. 9.1), what is happening to the kinetic energy of the system (neglecting friction)?
If the kinetic energy is decreasing, is there another form of mechanical energy in the system that may be increasing? If so, what is it?
Write an equation for the mechanical energy of the system at h2, and call it Eq. 3.
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Chapter 9 Solutions
Physics Laboratory Experiments
- Hello can you help me solve this problem with complete solution and illustration? *A 40kg boy is sliding on a horizontal and frictionless surface with an initial momentum of 90J due east. When t=0, a force, a function of time, F=8.20t is applied to the boy due west. a) at what value of t will result in the momentum of the boy 60J due west? b) what is the acceleration of the boy at the time computed in letter a?arrow_forwardInitially, ball 1 rests on an incline of height h, and ball 2 rests on an incline of height h/2 as shown in the figure below. They are released from rest simultaneously and collide elastically in the trough of the track. If m2 = 9m1, m1 = 0.040 kg, and h = 0.35 m, what is the velocity of each ball after the collision? (Assume the balls slide but do not roll. Indicate the direction with the sign of your answer. Positive is to the right, and negative is to the left. Due to the nature of this problem, do not use rounded intermediate values in your calculations—arrow_forwardStarting from Newton’s second law of motion, prove that impulse imparted on an object is equal to the change in momentum its momentum. Two masses m1 and m2 with a separation distance of d, attract each with a force F. What is the relationship between the F, m1, m2, and d? By what factor will the force of attraction change if the distance is quadrupled? A 400 kg object moving at a speed of 5 m/s to the right collides with a 600 moving at 2 m/s to the left. After the collision, the 600 kg object moves to the right at a speed of 3 m/s. Determine, the velocity of the 400 kg object after the collisionarrow_forward
- A container explodes and breaks into three fragments that fly off in one plane, indirections that make equal angles apart from one another. The resulting fragments have a massratio 1:5:1. What kind of process is this? Show the pictorial representation of the system (i.e., showthe vector momenta), and mark the known and unknown quantities that characterize this system. Show that the speeds of the first and third fragments must be equal. If the first piece flies off with a speed of 10.2 m/s, what is the speed of the second fragment?arrow_forwardA bullet having a mass of 0.05 kg, moving with a velocity of 400 m/s penetrates a distance o 0.1 m into a wooden block firmly attached to the earth. Assume the accelerating force constant, Compute.a) The acceleration of the bulletb) The accelerating forcec) The time of accelerationd) The impulse of the collision. Compare the answer to part (d) with initial momentum of the bulletarrow_forwardA block of mass M, capable of sliding with negligible friction over a horizontal air rail, is attached to one end of the rail by a spring of negligible mass and elastic constant k, initially relaxed. A projectile with mass m and horizontal velocity v, hits the block at t=0, as shown in the figure below; the projectile is attached to the block. The expression of the system's displacement X for t > 0 is:arrow_forward
- For the distribution of particles appearing in the plane of the figure, all particles have the same mass m. Determine: a) The coordinates of the center of mass of the systemb) The coordinates in which a fourth particle of mass 2m must be placed so that the center of mass of the new system moves to the origin of coordinates.arrow_forwardHow would you find the velocity of the cue ball after the collision? (Please include magnitude and direction). Also, would this be an elastic or inelastic collision?arrow_forwardProve that in a one-dimensional elastic collision of two equal masses, the particles simply exchange velocities during collisions.arrow_forward
- a mass m1 collides elastically with a mass m2 initially at rest in a 1-dimensional collision. if the velocity of m1 is vo before the collision, derive a formula for the velocities of m1 and m2 after the collisions. If m1 >> m2, what roughly is the speed of m2 after the collision?arrow_forwardLet it be a system formed by two particles 1 and 2 of mass m1 and m2, respectively. Show that the position of the center of mass is located at an internal point to the line segment that connects the positions of particles 1 and 2. This result allows us to immediately estimate the position of the center of mass of a two-particle system.arrow_forwardTwo billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball's initial speed was 2.50 m/sm/s, and the other's was 4.00 m/sm/s in the opposite direction, what will be their velocities after the collision? Enter your answers numerically separated by a comma. Enter positive value if the direction of the velocity is the same as the direction of the initial velocity of the first ball, and negative value if the direction of the velocity is opposite to the direction of the initial velocity of the first ball.arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning