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Torques

Torque is the tendency of a force to rotate an object about an axis. It is thought to twist an object. Torque is the measure of the turning force on an object such as a bolt of a flywheel. Torque is often denoted by the Greek letter tau.

The magnitude of torque depends on three quantities: the force applied, the length or the lever arm connecting the axis to the point of force application and the angle between the force vector and the lever arm. The equations of torque are as followed:

τ=r x F

τ=rFsinθ

Where τ is the torque vector, r is the displacement vector, F is the force vector, x denotes a cross product and ϴ is the angle between the force vector and the lever arm vector. The SI unit for torque is the newton metre (Nm).

Earth as a rigid axisymmetric body

The earth maybe considered as a rigid axisymmetric body with a small quadrupole deformation. (There are two problems (a) and (b)) (a) If the exterior gravitational potential is written as: V(r)=-M_e*G*1/r*[1-J(R_e/r)^2* P_2(costheta)] Here, M_e is the mass of the earth, R_e is the equatorial radius and theta the colatit

Load Test on a 3 Phase Induction Motor

To obtain and analyse the performance characteristics of a 3 phase induction motor by load test. A 3 phase Induction motor supplied with the rated voltage (110v) plus two more values 90v and 115v. (4 poles) (results attached) Please see other attachment for calculations questions. Please expand on the discussion of resul

Physics Lab: Fulcrum Measurements

1. Suspend the meter stick by a string from its center. 2. Notice carefully where it balances. It probably will not balance exactly at 50 cm. All distances must be measured to this point (called the fulcrum). 3. Hang a 200 g mass on one side and a 50 g mass on the other and adjust the distances from the fulcrum until the m

Statistics Problem Set: Probabilities and Distribution

1. The table below shows the total number of man-days lost to sickness during one week's operation of a small chemical plant. Showing all of your work, calculate the arithmetic mean and standard deviation of the number of lost days. Days Lost 1-3 4-6 7-9 10-12 13-15 Frequency 8 7 10

Calculation of Engine Power

A four wheeled vehicle is to have a total mass of 1.5 tonnes and two axels with its wheels each having a mass of 65kg and a radius of gyration 500mm. The wheel tread diameter is 950mm. The coefficient of rolling resistance between the wheels and the road is 0.3. Calculate the engine power required such that the vehicle will have

Pistons on a refrigeration compressor

A single acting refrigeration reciprocating compressor has six pistons pitched 100mm from each other on the shaft. The pair cranks on VW formation are positioned on 120 degrees apart from each other on the shaft and compression- suction sequence is in the order of 1-6, 2-5, and 3-4. Calculate the out of balance torque when the s

Magnetism Circular Region Displacement

(Please refer to the attachment for detailed description of the problems) 4. The figure shows a circular region of radius R = 3.00 cm in which a uniform displacement current id = 0.500 A is directed out of the page. (a) What is the magnitude of the magnetic field due to the displacement current at a radial distance of 2.0

Physics

21. Units and Dimentions [Please refer to the attachment for the problem] 22. You hear a sound with level 80.0 dB and you are located 10.0 m from the sound source. What is the power being emitted by the sound source? 23. There is a 1.2 m distance between a crest and an adjacent trough in a series of waves on the surface of

Magnitude of the force F applied tangentially

See attached figure.jpg The mechanism shown in the figure is used to raise a crate of supplies from a ship's hold. The crate has total mass 56 kg. A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.20 m and a moment of inertia = 3.0 kg*m^2 about the axle. The crate is suspended

Least amount of current through a coil

A wood cylinder of mass m = .250 kg and length L=.100m, with N =10.0 turns of wire wrapped around it longitudinally, so that the plane of the wire coil contains the long central axis of the cylinder. The cylinder is released on a plane inclined at an angle theta to the horizontal, with the plane coil parallel to the incline plan

Physics: Meter stick period of oscillation; piston maximum speed

41 A uniform meter stick swings about a pivot point which is a distance x = 27.4 cm from the end of the stick. What is its period of oscillation? 83 The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 0.66 m. If the piston moves with simple harmonic motion with an angular frequency of 180

Principle Stresses for Elements

The figure shows a schematic of typical steel (E=200GPa, v=0.3) kneed support. The shaft has a diameter of 16mm. The dimensions are a=150mm and b=300mm and the forces are F=100N, P=75N and P2=50N. At the wall, Kt=1.75 and Kts=2. Considering the Generalized Hooke's law: a. What are the principal stresses at the critical stress

General Questions: Six Questions to Learn Concepts

1. The Moon is centripetally accelerating towards the Earth. Explain why it is not getting closer to the Earth. 2. Why is it easier to hold a 10lb weight next to your body instead of with your arm outstretched? 3. When you design a building in an earthquake region, how should the natural frequencies of oscillation of the b

Cylinder of mass and radius is rolling on a stationary larger

A cylinder of mass m and radius a is rolling on a stationary larger cylinder of radius R. At what angle will the smaller cylinder will leave the surface and what is the friction force between the cylinders (assume coefficient mu). Please see the attached file for full problem description.

Angular motion of the baggage carousel

A baggage carousel at an airport is rotating with an angular speed of 0.18 rad/s when the baggage begins to be loaded onto it. The moment of inertia of the carousel is 1000.0 kgm2. Ten pieces of baggage with an average mass of 25.0 kg each are dropped vertically onto the carousel and come to rest at a perpendicular distance of 2

List and define each of Newton's Laws governing linear motion

3. List (by number and name) and define with words or equations each of Newton's Laws governing linear motion. Give a real life example illustrating each. 4. A person performs a standard long jump from the ground (takeoff and landing surfaces the same). Using a total flight time of 0.43 s and a horizontal displacement

Rotational Simple Harmonic Oscillation: Rod with two springs

A 1-dimensional rod 2 meters long of mass 60 grams uniformly distributed has an axle through its midpoint allowing the rod to rotate in a vertical plane. At each end of the rod are identical, ideal springs which have spring constants of 40 N/cm. At equilibrium the rod lies horizontally in the vertical plane. The rod is given

Three problems on forces.

A. A claw hammer is used to pull a nail out of a board. The nail is at a 60 degree angle of to the board, and a force F1 of magnitude 500N applied to the nail is required to pull it from the board. The hammer head contacts the board at point A, which is 0.080m from where the nail enters the board. A horizontal force F2 is appl

Friction on inclined plane

5. A rectangular block twice as high as it is wide is resting on a board. The coefficient of static friction between board and incline is .63. If the board is tilted will the block first tip over or begin sliding? 6. A uniform pole of mass M is at rest on an incline of angle secured by a horizontal rope. For what angle

Force

Please see the attached file. A horizontal boom 8 ft long is attached to a wall at its inner end and is supported at its outer end by a cable that makes an angle 30° with the boom. The boom weighs 60 lb, and a load of 500 lb is attached to its outer end. Find the (a) tension T in the cable and (b) the compression force F in

The cart shown starts from rest and rolls down the slope.

(Please refer attachment for fig) The cart shown starts from rest and rolls down the slope. For each wheel Ic = 0.8 ft-lb-s^2, weight 30 lb. and diameter 32 in. The body of the cart weighs 60 lb. Assuming no slipping and neglecting friction at the axles, determine the a) acceleration of the cart down the slope, b) minimum coe

Hydostatics: Force and torque on a dam wall of reservoir

As the reservoir behind a dam is filled with water, the pressure that the water exerts on the dam increases. Eventually, the force on the dam becomes substantial, and it could cause the dam to collapse. There are two significant issues to be considered: First, the base of the dam should be able to withstand the pressure rho gh,

Simple Harmonic Motion..

A slender, uniform metal rod of mass M and length l is pivoted without friction about an axis through its midpoint and perpendicular to the rod. A horizontal spring, assumed massless and with force constant k, is attached to the lower end of the rod, with the other end of the spring attached to a rigid support. a). Find the

To determine the torsional constant of a Torsional Pendulum.

A thin metal disk of mass m = 2 x 10^-3 kg and radius R = 2.20 cm is attached at its center to a long fiber. When the disk is turned from the relaxed state through a small angle theta, the torque exerted by the fiber on the disk is proportional to theta: T= -k*theta The constant of proportionality k is called the "torsional

Motion of objects on an inclined plane.

Object 1 rolls up the incline without slipping. Object 2 rolls down the incline without slipping. Object 1 is a solid sphere and has mass 2kg and radius R1 Object 2 is a hoop of mass 1kg and radius R2 Object 3 is a disk that is mounted on a frictionless axle through its CM. It has mass 4kg and radius R3 (this disk acts

Sliding Ladder

A uniform ladder with mass m_2 and length L rests against a smooth wall. A do-it-yourself enthusiast of mass m_1 stands on the ladder a distance d from the bottom (measured along the ladder). The ladder makes an angle theta with the ground. There is no friction between the wall and the ladder, but there is a frictional force of

A Bar Suspended By Vertical Strings

A rigid, uniform, horizontal bar of mass m_1 and length L is supported by two identical massless strings. Both strings are vertical. String A is attached at a distance d < L/2 from the left end of the bar and is connected to the ceiling; string B is attached to the left end of the bar and is connected to the floor. A small block