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1.Show that the force field vec F =(2xy-4- 1 2 sin( x 2 )sin( y 2 )) hat i +(x^ 2 + 1 2 cos( ...

cos( x 2 )cos( y 2 )) hat j is conservative and
obtain the potential function. Evaluate the work done by vec F in moving a particle along the curve C which is the portion of the circle centered at origin with radius 2 in the first quadrant with counter clockwise orientation, without using line integrals.

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2.A skier starts from rest at the top of a hill. The skier coasts down the hill and up a ...

as the drawing illustrates. The crest of the second hill is circular, with a radius of 28.6m. Neglect friction and air resistance. What must be the height of the first hill so that the skier just loses contact with the snow at the crest of the second hill?

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3.Q1) (15 points) In the diagram below, M1 = 50 Kg, M2 = 20 Kg, mass and radius of the ...

g and 30 cm each, respectively. Both M1 and M2 rest on frictionless surfaces and the system starts from rest.
(a) Draw the fbd for each of M1, M2 and the pulley.
(b) Write the equations of motion for each of M1, M2 and the pulley.
(c) Calculate the linear acceleration of the two masses, as well as the angular acceleration of the pulley.
(d) Calculate the angular velocity of the pulley after M1 and M2 have been displaced linearly by 2 m.
Q2) (10 points) A basketball is thrown with an initial speed v0 of 10.8 m/s at 400 above horizontal, and it enters the hoop from above. The ball is released at 2.00 m above the ground. The hoop is 3.05 m above the ground and 10.0 m away from the player.
(a) Find the time at which the ball passes through the hoop.
(b) Find the ball’s velocity (express in component form) just when it enters the hoop.
(c) Find the ball’s maximum height.
Q3) (5 Points) An object is thrown up from the top of a building of height of 400 m with an initial velocity of 20 m/s.
(a) Find the position and the velocity of the object 5 s later.
(b) With what velocity will it hit the ground?
(c) At the same time the first object is thrown up, a second object is thrown up from the ground at 100 m/s. Will the two objects collide? If yes, calculate when and where,

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in a circle, its perpendicular bisector, and the centre of the circle
• the measures of angles in circles

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5.A rock weighs 105 N on the surface of planet X with gx= 21.2 ms2 . What is the weight ...

the surface of planet Y, which has 29 times the mass and 3.6 times the radius of planet X?

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7.I am trying to figure out the optimal radius that will give the lowest surface area of a cylinder. I ...

have done the calculus which reveals that the surface area is at a minimum when height is double the radius. I am now trying to find an equation for the relationship between the amount of wasted surface area as a percentage of the minimum surface area and the ratio between height and radius.
If I were to plot it on a graph, the y axis would be the percentage of excess materials needed as a percentage of the minimum possible surface area, and the x axis would be height divided by radius. Since the surface area is minimized when height=2(radius), I know that when x=2, y=0.
The website https://www.datagenetics.com/blog/august12014/index.html explains what I am trying to do quite well and shows the graph below. I am trying to find the equation for this graph, but am unsure how to go about it.

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lculate surface area.
(b) Calculate total capacitance presented by the cell membrane.
(c) cell membrane has a resistance of 10 MΩ. Calculate τ
(d) interior of the cell has an initial potential of Vi = 0 V, a potential of Vo = 100V is applied to the outside of the cell. Calculate how long it takes for the potential inside the cell to reach 50 V.

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them on the ground. A dung beetle can roll (without slipping) a ball of dung with radius 4.70 cm at a linear speed of 8.90 cm/s.
Through what angle does the ball roll as the ball moves a distance of 10.0 cm?

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gle does the wheel rotate in 1.00 s?

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a) A scientific theory must be able to be proven.
b) A scientific theory has been derived from known facts and always applies.
c) A scientific method should give different results depending on who performs the method.
d) Knowledge of our surroundings usually emerges through an interplay between theory and experiment.
2) The sides of a straight block are measured to 3,202 cm; 0.0012 cm and 11.2 cm, respectively. Calculate the volume of the straightening block and enter it with the correct number of value digits.
(2/0/0)
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3) A 9.2 dm long and evenly thick rod rests on a support. 0.55 dm from one end, a dynamometer is hung so that the rod will hang horizontally. Then the dynamometer shows 4.4 N. How much does the bar weigh?
(1/1/0)
Number of words: 0
4) A bar AB that is homogeneous and evenly thick has a length of 2.70 m and is rotatable about an axis at A. The bar weighs 25 kg and is kept in equilibrium by a force F which has its point of attack in B. is 45 degrees. How big is the force F?
(1/1/0)
Saved!
25 * 9.82 = 245.5 N
Number of words: 6
5) A trolley rolls at a constant speed to the right. On the cart is an upward cannon that suddenly shoots a bullet. The carriage continues to the right with the same speed as before. Where does the bullet end up when it falls? For a detailed reasoning.
(1/1/1)
Number of words: 0
6) A river is 200 m wide. The water in the river flows at a speed of 2.5 m / s. A motorboat steers across the river at its maximum speed, which in stagnant water is 5.0 m / s. The boat is constantly heading perpendicular to the banks of the river. Where does the motorboat land on the other shore?
(2/0/0)
Number of words: 0
7) A ball with a mass of 2.0 hg moves at a constant speed in a circular path. The radius of the track is 1.5 m and it takes the ball 3.0 seconds to move one turn. How big is the centripetal force?
(1/1/0)
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8) A bullet moves at a constant speed. Can we then safely say that the resultant of the forces acting on the bullet is zero? Motivate and discuss your answer.
(0/1/1)
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9) A conductor is located between the poles of a permanent magnet. The current in the conductor goes in the direction of the plane of the paper (away from the reader). How is the force acting on the leader directed?
(1/0/0)
a) To the right of the figure
b) To the left in the figure
c) Downwards in the figure
d) Upwards in the figure
10) Protons enter horizontally from the left between two large metal plates at a speed v = 0.80 Mm / s. The plates are connected to a voltage source with the pole voltage U. Between the plates there is a homogeneous magnetic field with a flux density of 38 mT directed perpendicular to the plane of the paper. The distance between the plates is 1.5 cm. They want the protons to continue with unchanged direction and speed between the plates. Which of the plates should be connected to the positive pole of the voltage source and how large should the voltage U be?
(0/2/0)
Number of words: 0
11) The magnetic flux Φ through a 700-speed coil decreases linearly with time according to the diagram below. Calculate the voltage across the coil at time t = 1.0 ms.
12) The current in a coil with an inductance of 35 mH has a growth rate of 6.2 A / s at a given moment. What is the instantaneous value of the ems induced in the coil?

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but outside the triangle as a function of of the length 3x of the side of the triangle

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13.a) The volume of a right circular cylinder is V(x) = pi(x^3- 5x^2 + 8x- 4). Find the radius and ...

ht.
b) Explain the graph in the context of the problem.
b) Explain any restrictions on x in the context of the question.

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14.A sphere of mass M = 20kg and radius R = 10cm has its mass distributed in a way where ...

mediately guess it’s moment of inertia. To investigate whether it behaves more like a solid sphere or hollow sphere, you roll it down a rough ramp inclined at an angle of 30° with respect to the horizontal. The sphere rolls without slipping and you measure the velocity of the center of mass to be 3 m/s as it leaves the bottom of the ramp. The ramp’s length is 2 m and you release the sphere from the top of the ramp, a height of 1 m.
a) What is the moment of inertia of the sphere?
b) What is the angular speed of the sphere as it reaches the bottom of the ramp?
c) What is the frictional force on the sphere?

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kilometer. Find the radius of the region.

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16.Find the area of a circular sector with a central angle of 7(pi) over 6 and a radius of 12 ...

memphis, TN and New orleans, LA lie approximately on the same meridian. Memphis has a latitude of 35°N. find the distance between the 2 cities. (the radius of the earth is 3960 miles.)
Adam stands 30 ft from the base of a building and measures the angle of the elevation from the ground to the top of the building to be 57°. How tall is the building?

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17.I am wondering how to set up a multivariable integral under a surface, bound by a circle not set in ...

the origin? ie surface under some surface "f" as bound by the set: x^2+y^2-4x<0 (equivalent to: (x-2)^2 + y^2 < 4). My original thinking was to just translate the surface formula by the magnitude of the radius of this circle and assume the standart polar setup for cirles located at the origin, but this makes the integral very unpleasant. Could i get any suggestions for how to solve this?
Thanks

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18.I have this math problem which I hope one of you can help me with! -A giant circular fair ride has ...

a radius of 60m, with 12passenger pods spaced around the circumference at equal distances. How far is it directly from the sixth pod to the tenth pod?

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19.A circle with radius 8 has a chord AB marking off 135 degree central angle. What is the area of ...

portion of the circle between the chord and the circumference? No trigonometric ratios allowed.

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is uniformly distributed across thier cross section . calculate the magnetic field in the region ra

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22.I'm not sure how to write an equation for the area of the curved surface of a cylinder with only ...

sum of the radius and height.

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carrying a current of 3.77 A from the bottom of the page to the top, where a negative value indicates that the current is actually from the top of the page to the bottom. To the right of the first current is a circular current of 6.57 A in the counterclockwise sense, where a negative value indicates that the current actually flows in the clockwise sense. The radius of the circular current loop is 4.00 mm, and its center is 5.00 mm from the long, straight wire. What is the component of the magnetic field in the direction out of the page at the center of the circular current loop? As is very often the case, drawing the diagram is apt to help.

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onal radius of r = 0.010 m is used to connect two objects.
(a) What is the cross-sectional area of the wire?

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t one type of ball has a radius of
2.4
cm
. The length and width of the box's square base are both twice the radius, and the balls are packaged four to a box, so that the height is eight times the radius. Find the percentage of the box that is filled. Round your percentage to the nearest hundredth. Also round all intermediate calculations to four decimal places.
The percentage of the box that is filled, to the nearest hundredth, is
%

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st tenth of a centimetre.

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28.The mass of a wheel is 5 kg and its radius of duration is 0.25 m. What is its moment ...

produce an acceleration of 4 rad s^-1 what amount of torque is required to apply on it?

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30.The volume of a cylinder with height h and radius r can be found using the formula V = π ...

Suppose the volume of a cylinder is 402.12 ft3 and the height is twice the radius what is the radius of the cylinder. Determine the radius, rounded to the nearest whole foot.
The radius is____ ft?

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le with a radius of 15 km.
You begin your walk 20 km WEST and 5 km SOUTH of the center of the forest and walk directly toward the easternmost point of the forest. You walk at a constant speed of 5 km/hr.
How much time passes from the moment you enter the forest until you are at the point where you are closest to the center of the forest?
How do I do this?

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32.Suppose you are at the center of a circle with a radius of 1 mi. How far left or right ...

p or down must you move in order to end up on the boundary of the cycle, with a final angle of 22 degrees in standard position with respect to the horzontal axis?

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33.How do I solve a runner sprints along a circular track of radius 110m at a speed of 7m/s, runner's ...

riend is standing at a distance 220m from the center of the track, How fast is the distance between them changing if distance between them is 220m?

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at is, determine the radius and the height) that would maximize the volume of the cylinder. State your final answer accurate to 1 decimal place

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35.. A uniform cylinder of mass M and radius R is initially at rest on a rough horizontal surface. A ...

ght string is wrapped around the cylinder and is pulled straight up with a force T whose magnitude is 0.8 Mg. As a result, the cylinder slips and accelerates horizontally. The moment of
inertia of the cylinder is I = 12 MR2 and the coefficient of kinetic friction is 0.4.
a. On the diagram above show all the forces applied on the cylinder. b. Determine the linear acceleration a of the center of the cylinder. c. Determine the angular acceleration α of the cylinder.
d. Explain the difference in results of linear acceleration a and αR.

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36.A circle has a radius of .3.5in A sector of the circle has a central angle of 4.3 radians. Find ...

the area of the sector.
Do not round any intermediate computations. Round your answer to the nearest tenth.

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37.A sector of a circle of radius 6.5in has an area of 20in^2 Find the central angle of the sector. ...

not round any intermediate computations. Round your answer to the nearest tenth.

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38.A sector of a circle of radius 6.5in has an area of 20in^2 Find the central angle of the sector. ...

not round any intermediate computations. Round your answer to the nearest tenth.

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he radius is 0.05cm. Estimate the possible relative error in the area of the top of the cover.

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics