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Problem 2.1(10 points) A rod with mass m is starting to move from the initial vertical...
5. A particle of mass m slides without friction and starting from rest down a block...
5. A particle of mass m slides without friction and starting from rest down a block of mass M in which the surface is shaped into a quadrant of a circle of radius R. The block also slides without friction on a table top. Choose two suitable generalized coordinates a) Using the Lagrange-multiplier formalism, find the equations of motion of the mass and the block and the reaction force of the block on the mass (ie. the constraint force b)...
Question 4 A homogeneous slender rod AB of mass m and length L is held in...
Question 4 A homogeneous slender rod AB of mass m and length L is held in the position shown in Figure Q4. The end A of the rod is free to move along the smooth horizontal surface. The end B of the rod is connected to rod BC of negligible mass. The rod AB is released from rest in the position shown when 0 = 60°. If the acceleration of end B is ā, = -a,j, derive the expressions in...
A block (can be treated as point particle) of mass m is released from a vertical...
A block (can be treated as point particle) of mass m is released from a vertical height of h as shown in figure below. It slides down a frictionless surface and collides with a uniform vertical rod of mass M and length L After the collision they stick together and the system momentarily stops when the rod makes angle with respect to its initial position. Find ? in terms of m, M, L and h
Problem 3: The collar of mass m rest on a smooth rod, attached to two springs...
Problem 3: The collar of mass m rest on a smooth rod, attached to two springs of unstretched length I. If the collar is displaced a distance s and released from rest, determine its velocity at the instance it returns to the initial position s=0.
4(12 points) A uniform rod of length L and mass M is attached at one end...
4(12 points) A uniform rod of length L and mass M is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane as in Figure. The rod is released from rest in the horizontal position. (a)What are the initial angular acceleration of the rod and the initial translational acceleration of its right end (as shown in Fig.a)? (b)What is its angular speed when the rod reaches its lowest position (as...
Problem 2 (50 points) An object of mass m is launched from the ground at 30...
Problem 2 (50 points) An object of mass m is launched from the ground at 30 degrees to the horizontal with an initial velocity v. After achieving a height of 10 m it begins to fall. Precisely at this point, it also explodes into two pieces of equal mass; these two pieces initially move horizontally. One of the pieces comes back and lands precisely where the object started out. (a) What was the y component of the initial velocity v?...
18. In the previous problem, as the rod swings down freely from its initial position to...
18. In the previous problem, as the rod swings down freely from its initial position to the vertical position, what happens to the magnitude of the angular acceleration a and the magnitude of the angular velocity w? A lo increases and increases B. Jolstays constant and increases c la decreases and increases D la decreases and w decreases E la stays constant and (w stays constant
Problem 4: A projectile is fired with an initial velocity of 54.1 m/s, at an initial...
Problem 4: A projectile is fired with an initial velocity of 54.1 m/s, at an initial inclination of 33.7 degrees with the horizontal r-axis. All initial variables (displacement and time) start at 0. You are asked to consider two cases of motion for the projectile, one without drag, and one with drag, with both the cases including effects of gravity. a) For motion with no drag, acceleration vector is given as а -g, where g 9.8 m/s. b) For motion...
At the same instant that a 9.9 kg ball is dropped from 76 m above the...
At the same instant that a 9.9 kg ball is dropped from 76 m above the Earth's surface, a second ball, with a mass of 15.0 kg, is thrown straight upward from the Earth's surface with initial velocity of 8.86 They move along nearby vertical paths and pass without colliding. Calculate the position relative to the surface of the Earth of the center of mass of the two-ball system after 6.57 s. A negative answer is okay, can you interpret...
At the same instant that a 9.44 kg ball is dropped from 105 m above the...
At the same instant that a 9.44 kg ball is dropped from 105 m above the Earth's surface, a second ball, with a mass of 14.4 kg, is thrown straight upward from the Earth's surface with initial velocity of 9.8 . They move along nearby vertical paths and pass without colliding. Calculate the position relative to the surface of the Earth of the center of mass of the two-ball system after 3.79 s. A negative answer is okay, can you...
5. A particle of mass m slides without friction and starting from rest down a block of mass M in which the surface is shaped into a quadrant of a circle of radius R. The block also slides without friction on a table top. Choose two suitable generalized coordinates a) Using the Lagrange-multiplier formalism, find the equations of motion of the mass and the block and the reaction force of the block on the mass (ie. the constraint force b)...
Question 4 A homogeneous slender rod AB of mass m and length L is held in the position shown in Figure Q4. The end A of the rod is free to move along the smooth horizontal surface. The end B of the rod is connected to rod BC of negligible mass. The rod AB is released from rest in the position shown when 0 = 60°. If the acceleration of end B is ā, = -a,j, derive the expressions in...
A block (can be treated as point particle) of mass m is released from a vertical height of h as shown in figure below. It slides down a frictionless surface and collides with a uniform vertical rod of mass M and length L After the collision they stick together and the system momentarily stops when the rod makes angle with respect to its initial position. Find ? in terms of m, M, L and h
Problem 3: The collar of mass m rest on a smooth rod, attached to two springs of unstretched length I. If the collar is displaced a distance s and released from rest, determine its velocity at the instance it returns to the initial position s=0.
4(12 points) A uniform rod of length L and mass M is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane as in Figure. The rod is released from rest in the horizontal position. (a)What are the initial angular acceleration of the rod and the initial translational acceleration of its right end (as shown in Fig.a)? (b)What is its angular speed when the rod reaches its lowest position (as...
Problem 2 (50 points) An object of mass m is launched from the ground at 30 degrees to the horizontal with an initial velocity v. After achieving a height of 10 m it begins to fall. Precisely at this point, it also explodes into two pieces of equal mass; these two pieces initially move horizontally. One of the pieces comes back and lands precisely where the object started out. (a) What was the y component of the initial velocity v?...
18. In the previous problem, as the rod swings down freely from its initial position to the vertical position, what happens to the magnitude of the angular acceleration a and the magnitude of the angular velocity w? A lo increases and increases B. Jolstays constant and increases c la decreases and increases D la decreases and w decreases E la stays constant and (w stays constant
Problem 4: A projectile is fired with an initial velocity of 54.1 m/s, at an initial inclination of 33.7 degrees with the horizontal r-axis. All initial variables (displacement and time) start at 0. You are asked to consider two cases of motion for the projectile, one without drag, and one with drag, with both the cases including effects of gravity. a) For motion with no drag, acceleration vector is given as а -g, where g 9.8 m/s. b) For motion...
At the same instant that a 9.9 kg ball is dropped from 76 m above the Earth's surface, a second ball, with a mass of 15.0 kg, is thrown straight upward from the Earth's surface with initial velocity of 8.86 They move along nearby vertical paths and pass without colliding. Calculate the position relative to the surface of the Earth of the center of mass of the two-ball system after 6.57 s. A negative answer is okay, can you interpret...
At the same instant that a 9.44 kg ball is dropped from 105 m above the Earth's surface, a second ball, with a mass of 14.4 kg, is thrown straight upward from the Earth's surface with initial velocity of 9.8 . They move along nearby vertical paths and pass without colliding. Calculate the position relative to the surface of the Earth of the center of mass of the two-ball system after 3.79 s. A negative answer is okay, can you...
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