A uniform ramp, mass mr , is hinged at one end to a dock. It is held up by an empty floating barrel, mass mb (including internal air) and volume V. There is a vertical rod connected to the barrel, holding up the ramp. If the top of the barrel were even with the top of the water, the ramp would be horizontal. The density of the water is p (rho).
What is the maximum limiting mass for a person, mp ,
who could walk to the end of the ramp without it sinking? Answer in
terms of some or all of the variables provided.
Homework Answers
A 192kg uniform beam is hinged at one end, and the other end is supported by...
A 192kg uniform beam is hinged at one end, and the other end is supported by a cable that is 21 degrees to the vertical. The beam is 2 meters long, and is 14 degrees above the horizontal. Calculated the direction of the force in the hinge with respect to the horizontal. Assume the cable has no mass.
11. A uniform thin rod of length L and mass M, pivoted at one end as...
11. A uniform thin rod of length L and mass M, pivoted at one end as shown above, is held horizontal and then released from rest. Ignore all effects due to friction. (a) Find the angular speed of the rod as it sweeps through the vertical position. solution: 、13g / L (b) Find the force exerted on the rod by the pivot at this instant. solution Mg (c) Starting from the horizontal position, what initial angular speed would be needed...
2. (50 points) A uniform rod of length L and mass m is hinged to a wall at one end and suspended ...
2. (50 points) A uniform rod of length L and mass m is hinged to a wall at one end and suspended from the wall by a cable that is attached to the other end of the rod at an angle of B to the rod (see figure below). Assume the cable has zero mass. There is a contact force at the pivot on the rod. The magnitude and direction of this force is unknown. In this problem you will...
[7.] A uniform rod with mass M, length L, and moment of inertial with respect to...
[7.] A uniform rod with mass M, length L, and moment of inertial with respect to the center of mass Icm = MLis hinged at one end (point P) so that it can rotate, without friction, around a horizontal axis. The rod is initially held at rest forming an angle with the vertical (see figure) and then released. a) Find the moment of inertia Ip of the rod with respect to point P. b) Find the magnitude of the angular...
In Fig. 12-33, one end of a uniform beam of mass 40.0 kg is hinged to...
In Fig. 12-33, one end of a uniform beam of mass 40.0 kg is hinged to a wall: the other end is supported by a wire that makes angles theta = 30.0degree with both wall and beam. Find the tension in the wire and the magnitude and angle from the horizontal of the force of the hinge on the beam.
One end of a uniform 4.40-m-long rod of weight Fg is supported by a cable at...
One end of a uniform 4.40-m-long rod of weight Fg is supported by a cable at an angle of θ = 37° with the rod. The other end rests against the wall, where it is held by friction as shown in the figure below. The coefficient of static friction between the wall and the rod is μs = 0.580. Determine the minimum distance x from point A at which an additional object, also with the same weight Fg, can be...
(III) A uniform rod AB of length 5.0 m and mass M = 3.8 kg is...
(III) A uniform rod AB of length 5.0 m and mass M = 3.8 kg is hinged at A and held in equilibrium by a light cord, as shown in Fig. 9-67. A load W = 22 N hangs from the rod at a distance d so that the tension in the cord is 85 N. (a) Draw a free-body diagram for the rod. (b) Determine the vertical and horizontal forces on the rod exerted by the hinge. (c) Determine...
A toy consists of a uniform solid sphere of mass 200 g attached to the end...
A toy consists of a uniform solid sphere of mass 200 g attached
to the end of a uniform thin rod of mass 300 g , as shown in
(Figure 1). Together, the two objects are held upright on top of an
axle. The toy topples over and falls, with the rod ultimately
laying horizontally on a table.
What was the angular speed of the toy just before it hit the
table?
25cm 65cm
A thin, uniform, rectangular sign hangs vertically above the door of a shop. The sign is hinged to a stationary horizon...
A thin, uniform, rectangular sign hangs vertically above the door of a shop. The sign is hinged to a stationary horizontal rod along its top edge. The mass of the sign is 2.40 kg and its vertical dimension is 75.0 cm. The sign is swinging without friction, becoming a tempting target for children armed with snowballs. The maximum angular displacement of the sign is 25.0° on both sides of the vertical. At a moment when the sign is vertical and...
The diagram shows a thin rod of uniform mass distribution pivoted about one end by a...
The diagram shows a thin rod of uniform mass distribution pivoted about one end by a pin passing through that point. The mass of the rod is 0.290 kg and its length is 1.30 m. When the rod is released from its horizontal position, it swings down to the vertical position as shown. Determine the speed of its center of gravity at its lowest position. m/s When the rod reaches the vertical position, calculate the tangential speed of the free...
11. A uniform thin rod of length L and mass M, pivoted at one end as shown above, is held horizontal and then released from rest. Ignore all effects due to friction. (a) Find the angular speed of the rod as it sweeps through the vertical position. solution: 、13g / L (b) Find the force exerted on the rod by the pivot at this instant. solution Mg (c) Starting from the horizontal position, what initial angular speed would be needed...
2. (50 points) A uniform rod of length L and mass m is hinged to a wall at one end and suspended from the wall by a cable that is attached to the other end of the rod at an angle of B to the rod (see figure below). Assume the cable has zero mass. There is a contact force at the pivot on the rod. The magnitude and direction of this force is unknown. In this problem you will...
[7.] A uniform rod with mass M, length L, and moment of inertial with respect to the center of mass Icm = MLis hinged at one end (point P) so that it can rotate, without friction, around a horizontal axis. The rod is initially held at rest forming an angle with the vertical (see figure) and then released. a) Find the moment of inertia Ip of the rod with respect to point P. b) Find the magnitude of the angular...
In Fig. 12-33, one end of a uniform beam of mass 40.0 kg is hinged to a wall: the other end is supported by a wire that makes angles theta = 30.0degree with both wall and beam. Find the tension in the wire and the magnitude and angle from the horizontal of the force of the hinge on the beam.
(III) A uniform rod AB of length 5.0 m and mass M = 3.8 kg is hinged at A and held in equilibrium by a light cord, as shown in Fig. 9-67. A load W = 22 N hangs from the rod at a distance d so that the tension in the cord is 85 N. (a) Draw a free-body diagram for the rod. (b) Determine the vertical and horizontal forces on the rod exerted by the hinge. (c) Determine...
A toy consists of a uniform solid sphere of mass 200 g attached
to the end of a uniform thin rod of mass 300 g , as shown in
(Figure 1). Together, the two objects are held upright on top of an
axle. The toy topples over and falls, with the rod ultimately
laying horizontally on a table.
What was the angular speed of the toy just before it hit the
table?
25cm 65cm
The diagram shows a thin rod of uniform mass distribution pivoted about one end by a pin passing through that point. The mass of the rod is 0.290 kg and its length is 1.30 m. When the rod is released from its horizontal position, it swings down to the vertical position as shown. Determine the speed of its center of gravity at its lowest position. m/s When the rod reaches the vertical position, calculate the tangential speed of the free...
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