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Problem 13.39. The sphere al A is...
3. Under the influence of a vector field a particle spirals on the surface of a unit sphere toward the (t)-t and ф(t)- uppermost pole. With its spherical angular positions parametrically defined by 2...
3. Under the influence of a vector field a particle spirals on the surface of a unit sphere toward the (t)-t and ф(t)- uppermost pole. With its spherical angular positions parametrically defined by 24t, the particle's path can be defined t€[3m/2.2n. r(t)-sin(θ(t)) cos(d(t)) ị t sin(θ(t)) sin(φ(t))J+cos(θ(t)) k, Compute the work done by the constant vector field F(,y,z) 1 k in moving the particle along this path We were unable to transcribe this image
3. Under the influence of a...
PROBLEM 1 (10 POINTS) A uniform rope of weight W hangs between two trees. The ends...
PROBLEM 1 (10 POINTS) A uniform rope of weight W hangs between two trees. The ends of the rope are at the same height, and they each make angle 0 with the trees. Find a) the tension at either end of the rope b) The tension in the middle of the rope. PROBLEM 2 (10 POINTS) A particle of mass m moving along a straight line is acted on by a retarding force (one always directed against the motion) F-bea",...
PROBLEM 2 (10 POINTS) A particle of mass m moving along a straight line is acted...
PROBLEM 2 (10 POINTS) A particle of mass m moving along a straight line is acted on by a retarding force (one directed against the motion) F = beau, where b and a are constants and u is the velocity. At に0, it is moving with velocity 10. Find the velocity at later times always
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on...
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on an inclined plane with inclination angle ? in the gravitational field g. Follow the steps below to find the velocity V of the center of mass of the sphere as a function of time if the sphere is initially at rest. Bold font represents vectors. There exists a reaction force R at the point of contact between the sphere and the plane. The equations...
Could someone please help me with this problem? I would really appreciate it. 1.7. Consider the...
Could someone please help me with this problem? I
would really appreciate it.
1.7. Consider the vector field F(x,) = (ve" - 1 + xey a. Show that is a conservative force b. Find the potential function for F c. Find the work performed by the force field F on a particle that moves along the saw-tooth curve represented by the parametric equations: x = 1+ sin(sint) and y = (2/) sin(sin), with OSIS8r.
College Physics Problem. Please show all work An object with a mass of 4.55 kg starts...
College Physics Problem. Please show all work
An object with a mass of 4.55 kg starts from rest at point o and moves in the xy plane under the influence of the force F = (7xǐ + 2 N/m, where x and y are in meters y (m) (m Determine the work done on the object by the force as it moves along the paths listed below. (Include the sign of the values in your answers.) (a) path oC (b)...
4. Consider two particles of masses my and m2 and positions rı and r2 respectively. Suppose...
4. Consider two particles of masses my and m2 and positions rı and r2 respectively. Suppose m2 exerts a force F on mı. Suppose further that the two particles are in a uniform gravitational field g. (a) Write down the equations of motion for the two particles. (b) Show that the equations of motion can be written as MR = Mg ur = F where M is the total mass, R is the centre of mass, he is the reduced...
2. Consider a point particle of mass m undergoing a one-dimensional motion under the action of...
2. Consider a point particle of mass m undergoing a one-dimensional motion under the action of a force F(x) =-kx + az where k and ? are positive constants. Follow Example 3 in the lecture notes on Differential equations and discover an integral of motion I(x,v) - const for this mechanical system. Plot the integral curves (x, v) in phase space, by using the ContourPlot command in Mathematica to plot the lines of constant I(x,v). Set significance. (6 points)
GOAL Apply the basic definitions of work done by a constant force. PROBLEM An Eskimo returning...
GOAL Apply the basic definitions of work done by a constant force. PROBLEM An Eskimo returning from a successful fishing trip pulls a sled loaded with salmon. The total mass of the sled and salmon is 50.0 kg, and the Eskimo exerts a force of 1.20 102 N on the sled by pulling on the rope. (a) How much work does he do on the sled if the rope is horizontal to the ground (θ = 0° in the figure)...
Question 6.3 6.3 Consider a double mass-spring system with two masses of M and m on...
Question 6.3
6.3 Consider a double mass-spring system with two masses of M and m on a frictionless surface, as shown in Figure 6.30. Mass m is connected to M by a spring of constant k and rest length lo. Mass M is connected to a fixed wall by a spring of constant k and rest length lo and a damper with constant b. Find the equations of motion of each mass. (HINT: See Tutorial 2.1.) risto M wa ww...
3. Under the influence of a vector field a particle spirals on the surface of a unit sphere toward the (t)-t and ф(t)- uppermost pole. With its spherical angular positions parametrically defined by 24t, the particle's path can be defined t€[3m/2.2n. r(t)-sin(θ(t)) cos(d(t)) ị t sin(θ(t)) sin(φ(t))J+cos(θ(t)) k, Compute the work done by the constant vector field F(,y,z) 1 k in moving the particle along this path We were unable to transcribe this image
3. Under the influence of a...
PROBLEM 1 (10 POINTS) A uniform rope of weight W hangs between two trees. The ends of the rope are at the same height, and they each make angle 0 with the trees. Find a) the tension at either end of the rope b) The tension in the middle of the rope. PROBLEM 2 (10 POINTS) A particle of mass m moving along a straight line is acted on by a retarding force (one always directed against the motion) F-bea",...
PROBLEM 2 (10 POINTS) A particle of mass m moving along a straight line is acted on by a retarding force (one directed against the motion) F = beau, where b and a are constants and u is the velocity. At に0, it is moving with velocity 10. Find the velocity at later times always
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on an inclined plane with inclination angle ? in the gravitational field g. Follow the steps below to find the velocity V of the center of mass of the sphere as a function of time if the sphere is initially at rest. Bold font represents vectors. There exists a reaction force R at the point of contact between the sphere and the plane. The equations...
Could someone please help me with this problem? I
would really appreciate it.
1.7. Consider the vector field F(x,) = (ve" - 1 + xey a. Show that is a conservative force b. Find the potential function for F c. Find the work performed by the force field F on a particle that moves along the saw-tooth curve represented by the parametric equations: x = 1+ sin(sint) and y = (2/) sin(sin), with OSIS8r.
College Physics Problem. Please show all work
An object with a mass of 4.55 kg starts from rest at point o and moves in the xy plane under the influence of the force F = (7xǐ + 2 N/m, where x and y are in meters y (m) (m Determine the work done on the object by the force as it moves along the paths listed below. (Include the sign of the values in your answers.) (a) path oC (b)...
4. Consider two particles of masses my and m2 and positions rı and r2 respectively. Suppose m2 exerts a force F on mı. Suppose further that the two particles are in a uniform gravitational field g. (a) Write down the equations of motion for the two particles. (b) Show that the equations of motion can be written as MR = Mg ur = F where M is the total mass, R is the centre of mass, he is the reduced...
2. Consider a point particle of mass m undergoing a one-dimensional motion under the action of a force F(x) =-kx + az where k and ? are positive constants. Follow Example 3 in the lecture notes on Differential equations and discover an integral of motion I(x,v) - const for this mechanical system. Plot the integral curves (x, v) in phase space, by using the ContourPlot command in Mathematica to plot the lines of constant I(x,v). Set significance. (6 points)
Question 6.3
6.3 Consider a double mass-spring system with two masses of M and m on a frictionless surface, as shown in Figure 6.30. Mass m is connected to M by a spring of constant k and rest length lo. Mass M is connected to a fixed wall by a spring of constant k and rest length lo and a damper with constant b. Find the equations of motion of each mass. (HINT: See Tutorial 2.1.) risto M wa ww...
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