A copper rod (length = 1.3 m, radius = 3.70 103 m) hangs down from the ceiling. A 8.3kg object is attached to the lower end of the rod. The rod acts as a "spring", and the object oscillates vertically
63,141 results

Physics
A copper rod (length = 1.3 m, radius = 3.70 103 m) hangs down from the ceiling. A 8.3kg object is attached to the lower end of the rod. The rod acts as a "spring", and the object oscillates vertically with a small amplitude. Ignoring the rod's mass, find the frequency f of ... 
Physics(Simple Harmonic motion and Elasticity)
A copper rod (length = 2.0 m, radius = 3.0 * 10^3 m) hangs down from the ceiling. A 9.0kg object is attached to the lower end of the rod. The rod acts as a “spring,” and the object oscillates vertically with a small amplitude. Ignoring the rod’s mass, find the ... 
science
A steel rod of length 60 cm and radius 2.5 mm hangs vertically. If a mass of 2.5 kg is attached to the end of the rod, calculate the increase in the length of the rod 
Physics
A 2.5 m rod of mass M= 4. kg is attached to a pivot .8m from the left end so that it can rotate vertically. At the left end of the rod is a small object with mass m=1.5kg. A spring with a spring constant k=90N/m is attached to the right end of the rod. The other end of the ... 
College Physics
A rod of mass 4.3 kg and length 4.3 m hangs from a hinge as shown in Figure P9.28. The end of the rod is then given a “kick” so that it is moving at a speed of 2.3 m/s. How high will the rod swing? Express your answer in terms of the angle (in degree) that the rod makes ... 
college physics
I don't know where to begin with this question. Could someone help me please? A rod of mass 4.1 kg and length 1.6 m hangs from a hinge as shown in the figure below. The end of the rod is then given a "kick" so that it is moving at a speed of 5 m/s. How high will the rod swing... 
Math, Algebra
Rod a is twice as long as rod b, rod c is 1/12m shorter than rod b. If rod c is 1/6m long, find the total length of Rod a and Rod b I thought it would be 2x+(x+1/12)+1/6 
Physics
A 1.2 long steel rod with a diameter of 0.50 hangs vertically from the ceiling. An auto engine weighing 4.7 is hung from the rod. By how much does the rod stretch? 
physics
A cylindrical aluminum rod is attached to a wall by a hinge. A copper cable is attached to the rod at a point threequarters of its length away from the wall and used to support the rod in a horizontal position. The diameter of the rod is 5.0 cm and its unstressed length is 4.... 
Physics
A uniform rod of length L and mass M is held vertically with one end resting on the floor as shown below. When the rod is released, it rotates around its lower end until it hits the floor. Assuming the lower end of the rod does not slip, what is the linear velocity of the ... 
Physics
A 1.2m long steel rod with a diameter of 0.50cm hangs vertically from the ceiling. An auto engine weighing 4.7kN is hung from the rod. By how much does the rod stretch? 
Physics
A thin rod (length = 1.03 m) is oriented vertically, with its bottom end attached to the floor by means of a frictionless hinge. The mass of the rod may be ignored, compared to the mass of the object fixed to the top of the rod. The rod, starting from rest, tips over and ... 
math
Uniform rod AB with end B resting against rough vertical wall. Coefficient of friction between wall and rod is μ. Rod is 2m long and has mass 3kg. Rod is kept in limiting equilibrium by a light inextensible string, one end of which is attached to the end A of the rod and ... 
physics
Jahna and Raul move onto the setup for experiment 2. They have been asked to determine both the mass of the rod and the mass of the hanging object. They know the length of the rod, the position of the hanging mass, anf the positions and readings of the scales. Determine the ... 
physics
A uniform 1.3kg rod that is 0.80 m long is suspended at rest from the ceiling by two springs, one at each end of the rod. Both springs hang straight down from the ceiling. The springs have identical lengths when they are unstretched. Their spring constants are 60 N/m and 35 N... 
Physics
If a rod is moving at a velocity equal to 1/2 the speed of light parallel to its length, what will a stationary observer observe about its length? The length of the rod will become exactly half of its original value. The length of the rod remains the same. The length of the ... 
Physics  Science
Imagine a hollow sphere of radius R and mass M. It is welded to the end of a solid rod of length L, whose mass is also M. The rod is attached to the sphere in such a way that the whole assembly, when viewed from the side, looks like a lollipop. (That is, the axis of the rod, ... 
Physics 121
The disk has mass 10kg and radius 0.25m. The rod has mass 5kg, length 0.5m and radius 0.05m. The rod is split down the middle and is hinged so that its two halves can lay flat against the disk. Suppose that the disk and rod are initially rotating at 3.0rad/s around the axis ... 
Physics 121
The disk has mass 10kg and radius 0.25m. The rod has mass 5kg, length 0.5m and radius 0.05m. The rod is split down the middle and is hinged so that its two halves can lay flat against the disk. Suppose that the disk and rod are initially rotating at 3.0rad/s around the axis ... 
rotational mechanics
a thin rod of length 2R and mass M is standing vertically on a perfectly smooth floor. the state of equilibrium in which the rod at rest is unstable and the rod falls. FInd the trajectories that the various points of rod describe and velocity with which the upper end of rod ... 
physics
If a rod is moving at a velocity equal to 1/2 the speed of light parallel to its length, what will a stationary observer observe about its length? The length of the rod will become exactly half of its original value. The length of the rod remains the same. The length of the ... 
Physics
A mass of 100g is attached to one end of a massless rod, 10cm in length, which is pivoted about the opposite end. The rod is held vertical, with the mass at the top, and released. The rod swings. A. What is the speed of the mass at the instant that the rod is horizontal? B. ... 
physics
A mobile is constructed from a thin rod of mass 50 g and length 50 cm. Two hanging masses are positioned at each end of the rod. The mass of one of the hanging masses is 100 g. What must be the mass of the other hanging mass so that the mobile is in static equilibrium with the... 
physics
A mobile is constructed from a thin rod of mass 50 g and length 50 cm. Two hanging masses are positioned at each end of the rod. The mass of one of the hanging masses is 100 g. What must be the mass of the other hanging mass so that the mobile is in static equilibrium with the... 
Physics
One end of a thin uniform rod, 1.00m in length, is attached to a pivot. The rod is free to rotate about the pivot without friction or air resistance. Initially, it is hanging straight down (the "6 o' clock position). Then the lower tip is given an initial horizontal speed of ... 
physics
A uniform rod is set up so that it can rotate about a perpendicular axis at one of its ends. The length and mass of the rod are 0.849 m and 1.17 kg. What constantmagnitude force acting at the other end of the rod perpendicularly both to the rod and to the axis will accelerate... 
Physics
According to the Guinness Book of World Records (1990 edition, p. 169), the highest rotary speed ever attained was 2010 m/s (4500 mph). The rotating rod was 15 cm (5.9 in) long. Assume the speed quoted is that of the end of the rod. What is the centripetal acceleration of the ... 
Physics
Consider a lever rod of length 7.96 m, weight 71 N and uniform density. The lever rod is pivoted on one end and is supported by a cable attached at a point 1.74 m from the other end: ￼￼￼￼￼ ￼￼￼￼The lever rod is in equilibrium at angle of 54◦ from the ... 
College Physics Help
A thin rod (length = 1.10 m) is oriented vertically, with its bottom end attached to the floor by means of a frictionless hinge. The mass of the rod may be ignored, compared to the mass of the object fixed to the top of the rod. The rod, starting from rest, tips over and ... 
physics
One end of a thin rod is attached to a pivot, about which it can rotate without friction. Air resistance is absent. The rod has a length of 0.48 m and is uniform. It is hanging vertically straight downward. The end of the rod nearest the floor is given a linear speed v0, so ... 
Calculus
Let the length of a rod be 10 meters and the linear density of the rod ρ(x) be written in the form ρ(x) = ax + b with x = 0 representing the left end of the rod and x = 10 representing the right end of the rod. If the density of the rod is 2kg/m at the left end and 17 kg/m ... 
physics
A cylindrical rod( length L, radius R and density d) is dipped vertically in to a liquid. the rod is connected by a wire to a balance that measures the force to lift the rod. the contact angle between rod and liquid is θ. If rod is partially immersed so 0.5L is above the ... 
physics
A cylindrical rod( length L, radius R and density d) is dipped vertically in to a liquid. the rod is connected by a wire to a balance that measures the force to lift the rod. the contact angle between rod and liquid is θ. If rod is partially immersed so 0.5L is above the ... 
physics please help
One end of a thin rod is attached to a pivot, about which it can rotate without friction. Air resistance is absent. The rod has a length of 0.59 m and is uniform. It is hanging vertically straight downward. The end of the rod nearest the floor is given a linear speed v0, so ... 
physics
The figure shows an overhead view of a 3.00kg plastic rod of length 1.20 m on a table. One end of the rod is attached to the table, and the rod is free to pivot about this point without friction. A disk of mass 37.0 g slides toward the opposite end of the rod with an initial ... 
Physics
Suppose you’re building a contraption which contains a solid rod of length L = 12.5 m and mass 4.9 kg. This rod has its lower end barely above the ground at an angle of 20.6 degrees with respect to the horizontal, and is ultimately held up by a rope connected at a distance L... 
Physics
The length of the rod will become exactly half of its original value. The length of the rod remains the same. The length of the rod will decrease. The length of the rod will increase. Wouldn't the length double, thus being answer D? 
Physics
The length of the rod will become exactly half of its original value. The length of the rod remains the same. The length of the rod will decrease. The length of the rod will increase. Wouldn't the length double, thus being answer D? 
physics
A uniform rod of mass M = 0.245kg and length L = 0.49m stands vertically on a horizontal table. It is released from rest to fall. (a) Calculate the angular speed of the rod, the vertical acceleration of the moving end of the rod, and the normal force exerted by the table on ... 
Physics
a uniform rod of 3 kg and length 1 m is suspended from a fixed point by means of strings of length .8m and .6m which are attached to the free ends of the rod such that rod is horizontal. find the tensions in the string 
Physics
A point charge of charge 1 mC and mass 100 g is attached to a nonconducting massless rod of length 10 cm. The other end of the rod is attached to a twodimensional sheet with uniform charge density σ and the rod is free to rotate. The sheet is parallel to the yz plane (... 
Physics
A point charge of charge 1 mC and mass 100 g is attached to a nonconducting massless rod of length 10 cm. The other end of the rod is attached to a twodimensional sheet with uniform charge density σ and the rod is free to rotate. The sheet is parallel to the yz plane (... 
physics
A thin rod of mass M and length L is lying on a frictionless table. It is given an impulse of 4.5 N*s by a force of magnitude F on one end at an angle of 35 degrees to the rod. How far will the center of mass of the rod travel when the rod has completed 12 revolutions? 
Physics
The length of the rod will become exactly half of its original value. The length of the rod remains the same. The length of the rod will decrease. The length of the rod will increase. Wouldn't the length double, thus being answer D? No one has answered this question yet. 
Physics
The sketch shows a mobile in equilibrium. Each of the rods is 0.16 m long, and each hangs from a supporting string that is attached one fourth of the way across it. The mass of each rod is 0.10 kg. The mass of the strings connecting the blocks to the rods is negligible. What ... 
Pyhsic...Elena,please help....
A point charge of charge 1 mC and mass 100 g is attached to a nonconducting massless rod of length 10 cm. The other end of the rod is attached to a twodimensional sheet with uniform charge density σ and the rod is free to rotate. The sheet is parallel to the yz plane (... 
physics
A uniform thin rod of length 0.55 m and mass 5.5 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is a rest when a 3.0g bullet traveling in the horizontal plane of the rod is fired into one end of the rod. As viewed from above, the ... 
Physics
A long thin rod of mass M = 2:00 kg and length L = 75:0 cm is free to rotate about its center as shown. Two identical masses (each of mass m = .403 kg) slide without friction along the rod. The two masses begin at the rod's point of rotation when the rod is rotating at 10.0 ... 
Physics Angular Momentum
A long thin rod of mass M=2.00 kg and length L=75.0 cm is free to rotate about its center. Two identical masses (each of mass m = .45kg) slide without friction along the rod. The two masses begin at the rod's point of rotation when the rod is rotating at 10.0 rad/s. A) When ... 
physics
A thin nonuniform rod of length L=2.00 m and mass M=9.00 kg is free to pivot about an axis at one end. The CM of the rod is at a distance d=1.30 m from that end as illustrated below. The rod's moment of inertia about an axis through its CM and parallel to the rotation axis is... 
physics
A thin rod has a length of 0.25 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.33 rad/s and a moment of inertia of 1.40 103 kg · m2. A bug standing on the axis ... 
physics
a 51.0 kg uniform square sign, of edge L = 2.00 m, is hung from a horizontal rod of length dh = 3.00 m and negligible mass. A cable is attached to the end of the rod and to a point on the wall at distance dv = 4.00 m above the point where the rod is hinged to the wall. 
Physics
A cylinderical brass rod with a radius of 2.10 cm and length of 1.50 m is placed in a fire with temperature of 490 deg. C. If the other end of the rod is at a temperature of 33 deg. C, what is the rate of heat transfer through the rod (ignore any heat loss from the sides of ... 
AP Physics
A uniform thin rod of length 0.3m and mass 3.5kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3g bullet traveling in the horizontal plane of the rod is fired into one end of the rod. As viewed from above, the direction of... 
physics
A rod is nailed (flexibly) to a wall at one end. The other end is held up from letting the rod swing by a thread connected to the ceiling. The rod has mass M and length l. The moment of inertia is (Ml^2)/3. Determine the magnitude and direction of the force exerted on the rod ... 
PHYSICS
A thin rod has a length of 0.339 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.687 rad/s and a moment of inertia of 1.03 x 103 kg·m2. A bug standing on the ... 
PHYSICS
A thin rod has a length of 0.339 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.687 rad/s and a moment of inertia of 1.03 x 103 kg·m2. A bug standing on the ... 
Physics
A nonuniform 2.0kg rod is 2.0 m long. The rod is mounted to rotate freely about a horizontal axis perpendicular to the rod that passes through one end of the rod. The moment of inertia of the rod about this axis is 4.0 kg m2. The center of mass of the rod is 1.2 m from the ... 
physics
If an observer is traveling parallel to a rod at twice the speed of the rod, what is does the observer perceive the length to be? Choose one answer. a. The length of the rod remains the same. b. The length of the rod will become twice its original value. c. The length of the ... 
physics
If an observer is traveling parallel to a rod at twice the speed of the rod, what is does the observer perceive the length to be? Choose one answer. a. The length of the rod remains the same. b. The length of the rod will become twice its original value. c. The length of the ... 
Angular Momentum
A long thin rod of mass M = 2.00 kg and length L = 75.0 cm is free to rotate about its center as shown. Two identical masses (each of mass m = .421 kg) slide without friction along the rod. The two masses begin at the rod's point of rotation when the rod is rotating at 10.0 ... 
physics
A uniform rigid rod of mass 1kg and length 30cm. Find the moment of inertia of the rod about an axis perpendicular to the rod through on end. 
physics
A massless rod of length 1.00 m has a 2.00kg mass attached to one end and a 3.00kg mass attached to the other. The system rotates about a fixed axis perpendicular to the rod that passes through the rod 30.0 cm from the end with the 3.00kg mass attached. The kinetic energy ... 
Physics Please Help
A point charge of charge 1 mC and mass 100 g is attached to a nonconducting massless rod of length 10 cm. The other end of the rod is attached to a twodimensional sheet with uniform charge density σ and the rod is free to rotate. The sheet is parallel to the yz plane (... 
physics
A rod of length L = 1.2 m pivots freely about one end. The rod is held horizontally and released, with no intial velocity. Find the angular velocity of the rod as it passes through the vertical orientation. (Use conservation of energy. The rotational inertia of a rod like this... 
physics!!!
A copper rod is given a sharp compressional blow at one end. The sound of the blow, traveling through air at 2.79 degrees Celsius, reaches the opposite end of the rod 9.39ms later than the sound transmitted through the rod. What is the length of the rod? The speed of sound in... 
Physics
An object is formed by attaching a uniform, thin rod with a mass of mr = 6.54 kg and length L = 5.12 m to a uniform sphere with mass ms = 32.7 kg and radius R = 1.28 m. Note ms = 5mr and L = 4R. 1)What is the moment of inertia of the object about an axis at the left end of the... 
Collage Physic
A uniform rod hangs vertically on a frictionless horizontal axle passing through its center. The rod is 35cm long and 85g. A 15g ball of clay travelling horizontally at 2.5cm/s hits and sticks to the bottom of the rod. What is the maximum angle the rod makes with the vertical ... 
Physic
Can some one help me with this question. A uniform 119.0 cm long, 78.0 gram wooden rod is suspended from it midpoint. On one end of the rod, a mass of 350 g is attached, and on the other end a mass of 150 g is attached. A third mass of 225 g is attached at some distance x from... 
physics
A copper rod of length 0.83 m is lying on a frictionless table (see the drawing). Each end of the rod is attached to a fixed wire by an unstretched spring that has a spring constant of k = 73 N/m. A magnetic field with a strength of 0.17 T is oriented perpendicular to the ... 
physics
An object is formed by attaching a uniform, thin rod with a mass of mr = 6.54 kg and length L = 5.12 m to a uniform sphere with mass ms = 32.7 kg and radius R = 1.28 m. Note ms = 5mr and L = 4R. 1)What is the moment of inertia of the object about an axis at the left end of the... 
Physics
A thin, uniform rod is hinged at its midpoint. To begin with, one half of the rod is bent upward and is perpendicular to the other half. This bent object is rotating at an angular velocity of 6.8 rad/s about an axis that is perpendicular to the left end of the rod and parallel... 
physics
A thin, uniform rod is hinged at its midpoint. To begin with, onehalf of the rod is bent upward and is perpendicular to the other half. This bent object is rotating at an angular velocity of 7.1 rad/s about an axis that is perpendicular to the left end of the rod and parallel... 
Waves
a long fishing rod is kept upright .A boat engine causes the rod to vibrate.Mary speculates that the end of the rod moves to and fro 20 times in 1 minute.The amplitude of the vibrtion is 0.15m.Calculate the speed of the vibration at the end of the fishing rod 
physics
Calculate the angular speed of the rod, the vertical acceleration of the moving end of the rod, and the normal force exerted by the table on the rod as it makes an angle θ = 49.6° with respect to the vertical. b) If the rod falls onto the table without slipping, find the... 
physics
The 4.00kg block in the figure is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended towards the rod and each have a length of 1.25. The length from the upper string and lower string on the rod is 2... 
physics
The figure shows an overhead view of a uniform 2.00kg plastic rod of length 1.20 m on a very slick table. One end of the rod is attached to the table, and the rod is free to pivot about this point without friction. A disk of mass 36.0 g slides without friction toward the ... 
Phy 231
A baton consists of a nearly massless rod of length L and two spheres attached to the end of the rod, whose masses are each M and whose centers are separated by L. The spheres have radius R. If the sphere radius R is not negligible compared to the length L, what is the moment ... 
physics
When the temperature of a thin silver [α = 19 × 106 (C°)1] rod is increased, the length of the rod increases by 3.6 × 103 cm. Another rod is identical in all respects, except that it is made from gold [α = 14 × 106 (C°)1]. By how much ΔL does the length of the ... 
Physics
The left end of a 1kg, 1.0 m long uniform thin rod is attached to a pivot, about which it can rotate freely. A force F is applied at the right end of the rod at 30 degree angle to hold the rod stationary in a horizontal position. What is the magnitude of the force F? I think ... 
Physics
In the figure, a thin uniform rod of mass m = 3.05 kg and length L = 1.11 m rotates freely about a horizontal axis A that is perpendicular to the rod and passes through a point at a distance d = 0.201 m from the end of the rod. The kinetic energy of the rod as it passes ... 
Physics
A uniform metal rod, with a mass of 3.7 kg and a length of 1.2 m, is attached to a wall by a hinge at its base? A horizontal wire bolted to the wall 0.51 m above the base of the rod holds the rod at an angle of 25 degrees above the horizontal. The wire is attached to the top ... 
physics
A steel rod of length 1 m is welded to the end of an aluminum rod of length 2 m (lengths measured at 23 °C). The combination rod is then heated to 198 °C. What is the length of the combination rod at 198 °C? (The linear expansion coefficients for steel and aluminum are 1.3 ... 
physics
A thin, rigid, uniform rod has a mass of 2.60 kg and a length of 1.69 m. (a) Find the moment of inertia of the rod relative to an axis that is perpendicular to the rod at one end.A thin, rigid, uniform rod has a mass of 2.60 kg and a length of 1.69 m. 
physics
A long, straight metal rod has a radius of 4.50 cm and a charge per unit length of 30.0 nC/m. Find the electric field at the following distances from the axis of the rod, where distances are measured perpendicular to the rod. a)3.00 cm b)13.5 cm c)120 cm 
Physics
A long, straight metal rod has a radius of 6.00 cm and a charge per unit length of 36.0 nC/m. Find the electric field at the following distances from the axis of the rod, where distances are measured perpendicular to the rod. (a) 1.50 cm N/C (b) 13.5 cm N/C (c) 125 cm N/C 
Physics II
A copper rod of length 0.83 m is lying on a frictionless table (see the drawing). Each end of the rod is attached to a fixed wire by an unstretched spring whose spring constant is k = 79 N/m. A magnetic field with a strength of 0.13 T is oriented perpendicular to the surface ... 
physics
Determine the elongation of the rod in if it is under a tension of 5.7E10^3 N. The rod is made of aluminum and copper. From the aluminum to the copper section it measures 1.3m and from the copper section to the end it measures 2.6m with a radius of 0.2cm. Can someone please ... 
physics
Determine the elongation of the rod in if it is under a tension of 5.7E10^3 N. The rod is made of aluminum and copper. From the aluminum to the copper section it measures 1.3m and from the copper section to the end it measures 2.6m with a radius of 0.2cm. Can someone please ... 
physic
A rod is 2.40 m long and has a diameter of 2.50 mm. A force of 2000 N is applied to the end to stretch the rod by 1.40 mm. What is the tensile modulus for this rod? 
pls help physics problem
A 0.230kg wooden rod is 1.55 m long and pivots at one end. It is held horizontally and then released. 1) What is the angular acceleration of the rod after it is released? three sf with units 2) What is the linear acceleration of a spot on the rod that is 1.02 m from the axis ... 
Physics
A uniform metal rod, with a mass of 3.0 kg and a length of 1.0 m, is attached to a wall by a hinge at its base. A horizontal wire bolted to the wall 0.64 m above the base of the rod holds the rod at an angle of 40 degrees above the horizontal. The wire is attached to the top ... 
college student
Two spheres of mass 2 kg and 3 kg are attached to the ends of a light rigid rod of length 1.0 m. What is the moment of inertia of the system about an axis perpendicular to the rod and (i) passes through the centre of the rod (ii) passes through the 2 kg sphere 
Physics
A 1.34‒kg ball is attached to a rigid vertical rod by means of two massless strings each 1.70 m long. The strings are attached to the rod at points 1.70 m apart. The system is rotating about the axis of the rod, both strings being taut and forming an equilateral triangle... 
physics
An aluminum rod is 21.5 cm long at 20°C and has a mass of 350 g. If 12500 J of energy is added to the rod by heat, what is the change in length of the rod? 
Physics
There is a sign hanging off of a building. The sign itself is hung at the far end of a rod. The rod is held up by both a pivot on the building's wall, and a vertical cable attached 1 m away from the building to the rod. The cable and the rod make a right angle. The rod has ... 
Physics
A uniform rod of mass 2.0 kg and length 8.4 m is free to rotate about one end (see the following figure). If the rod is released from rest at an angle of 60° with respect to the horizontal, what is the speed (in m/s) of the tip of the rod as it passes the horizontal position? 
Physics
One end of a uniform 3.20mlong 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... 
Physics
There is a horizontal rod of length L and mass M. A point mass m is vertically above the rod at a vertical distance L/4 and horizontal distance L/3 from one end of the rod.Using The Riemann sum Integral,find the magnitude and direction of the gravitational force exerted on the... 
Math
There is a horizontal rod of length L and mass M. A point mass m is vertically above the rod at a vertical distance L/4 and horizontal distance L/3 from one end of the rod.Using The Riemann sum Integral,find the magnitude and direction of the gravitational force exerted on the...