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5. Blocks of mass m and 2m are free to slide without friction on a horizontal...
1. The small mass m is to slide down the large mass M without friction. The...
1. The small mass m is to slide down the large mass M without friction. The track along which the small block slides is a quarter circle with radius R. The large mass itself is free to move on a frictionless horizontal surface. Initially both masses are at rest with the small mass at the top of the quarter circle, as shown in the figure. (a) (5 Pts.) What is the initial total mechanical energy with respect to the horizontal...
15. Three blocks of mass M, 2M and 3M are shown. The middle block (2M) sits...
15. Three blocks of mass M, 2M and 3M are shown. The middle block (2M) sits on a frictionless table tipped at an angle o with the horizontal as shown. The other two blocks are connected to it by massless unstretchable strings that run over frictionless pulleys. At time t O the system is released from rest. Find: a) The magnitude of the acceleration of the blocks. b) The tensions Ti and T2 in the strings as indicated. T 2M...
(30pt) Two blocks connected by a spring of spring constant k are free to slide friction-...
(30pt) Two blocks connected by a spring of spring constant k are free to slide friction- lessly along a horizontal surface, as shown in Fig. 1. The unstretched length of the spring is a ure 1: Two masses connected by a spring sliding horizontally along a frictionless surface. (a) (10pt) Identify a set of generalized coordinates and write the Lagrangian. (b) (10pt) Find the equations of motion. (c) (10pt) Find a complete solution to the equations of motion
1. A block of mass m moves without friction on a horizontal plane. The body is...
1. A block of mass m moves without friction on a horizontal plane. The body is connected to a massless string which slides without friction over a fixed pulley. A massless pulley is fastened at the other end of the string. Over the pulley, which can rotate without friction, hangs another string which has two bodies of masses 3m and m fastened to its two ends respectively. Their motions are supposed to be strictly vertical. The acceleration of gravity is...
4. A particle of mass m is constrained to slide without friction on the surface of...
4. A particle of mass m is constrained to slide without friction on the surface of a smooth circular bowl of mass M with inner radius R as shown in the figure. The bottom of the bowl lies on a horizontal table and is free to slide without friction along the table. All motion is constrained to the plane of the page. Assume uniform gravitati acceleration. =T-V- State the Lagrangian for this system. Derive the differential equations of motion for...
An ideal spring is used to stop blocks as they slide along a table without friction....
An ideal spring is used to stop blocks as they slide along a table without friction. A 0.70 kg block traveling at a speed of 1.6 m/s can be stopped over a distance of 0.12 m once it makes contact with the spring. A rectangular block on a level surface moves at velocity v to the right towards a spring that rests on the surface and is attached to a fixed mount on the right. What distance would a 1.40...
Blocks A (mass 3.00 kg ) and B (mass8.00 kg ) move on a frictionless, horizontal...
Blocks A (mass 3.00 kg ) and B (mass8.00 kg ) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 3.00 m/s . The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and after the collision is along a straight line. Let +x be the direction of the initial motion of block A. A. Find the maximum energy stored in the spring...
Blocks A (mass 4.50 kg) and B (mass 15.00 kg) move on a frictionless, horizontal surface....
Blocks A (mass 4.50 kg) and B (mass 15.00 kg) move on a frictionless, horizontal surface. Initially, block B is at rest and block A is moving toward it at 1.00 m/s.The blocks are equipped with ideal spring bumpers. The collision is head-on, so all motion before and after the collision is along a straight line. Let +x be thedirection of the initial motion of AFind the maximum energy stored in the spring bumpers and the velocity of each block...
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without...
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without friction as in the figure. The bead is connected to an ideal spring of spring constant k, and the other end of the spring is connected to a fixed point at a perpendicular distance d from the wire. Unstretched length of the spring is very small, and can be taken to be zero. a) What is the period of oscillations of the bead around...
An ideal spring is used to stop blocks as they slide along a table without friction....
An ideal spring is used to stop blocks as they slide along a table without friction. A 0.75 kg block traveling at a speed of 2.2 m/s can be stopped over a distance of 0.12 m once it makes contact with the spring V What distance would a 1.10 kg block travel after making contact with the spring if the block is traveling at a speed of 3.0 m/s before it makes contact with the spring?
1. The small mass m is to slide down the large mass M without friction. The track along which the small block slides is a quarter circle with radius R. The large mass itself is free to move on a frictionless horizontal surface. Initially both masses are at rest with the small mass at the top of the quarter circle, as shown in the figure. (a) (5 Pts.) What is the initial total mechanical energy with respect to the horizontal...
15. Three blocks of mass M, 2M and 3M are shown. The middle block (2M) sits on a frictionless table tipped at an angle o with the horizontal as shown. The other two blocks are connected to it by massless unstretchable strings that run over frictionless pulleys. At time t O the system is released from rest. Find: a) The magnitude of the acceleration of the blocks. b) The tensions Ti and T2 in the strings as indicated. T 2M...
(30pt) Two blocks connected by a spring of spring constant k are free to slide friction- lessly along a horizontal surface, as shown in Fig. 1. The unstretched length of the spring is a ure 1: Two masses connected by a spring sliding horizontally along a frictionless surface. (a) (10pt) Identify a set of generalized coordinates and write the Lagrangian. (b) (10pt) Find the equations of motion. (c) (10pt) Find a complete solution to the equations of motion
1. A block of mass m moves without friction on a horizontal plane. The body is connected to a massless string which slides without friction over a fixed pulley. A massless pulley is fastened at the other end of the string. Over the pulley, which can rotate without friction, hangs another string which has two bodies of masses 3m and m fastened to its two ends respectively. Their motions are supposed to be strictly vertical. The acceleration of gravity is...
4. A particle of mass m is constrained to slide without friction on the surface of a smooth circular bowl of mass M with inner radius R as shown in the figure. The bottom of the bowl lies on a horizontal table and is free to slide without friction along the table. All motion is constrained to the plane of the page. Assume uniform gravitati acceleration. =T-V- State the Lagrangian for this system. Derive the differential equations of motion for...
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without friction as in the figure. The bead is connected to an ideal spring of spring constant k, and the other end of the spring is connected to a fixed point at a perpendicular distance d from the wire. Unstretched length of the spring is very small, and can be taken to be zero. a) What is the period of oscillations of the bead around...
An ideal spring is used to stop blocks as they slide along a table without friction. A 0.75 kg block traveling at a speed of 2.2 m/s can be stopped over a distance of 0.12 m once it makes contact with the spring V What distance would a 1.10 kg block travel after making contact with the spring if the block is traveling at a speed of 3.0 m/s before it makes contact with the spring?
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