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# Equilibrium

### Newtons law

Question 3 What force is required to give mass m = 40 kg acceleration a = 2 m/c2 ? Answer 60 N 80 N 40 N 20 N Question 4 What force is required to keep mass m = 20 kg moving with a constant speed along straight line? Answer 100 N 80 N 60 N

### Hanging speaker: What is the tension in each of the cables?

See Picture attached. A loudspeaker of mass 25.0 kg is suspended a distance of h= 1.00m below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of l= 4.00 m. What is the tension in each of the cables?

### Thermodynamics of the Carnot Cycle

1. An ideal gas operates in a Carnot cycle so. that it produces a net positive work of 400joules per cycle. The maximum temperature during the cycle is 300 °C and the heat lost to a low temperature bath is 600 joules per cycle. a) What must be the temperature of the low temperature bath? b) What is the change in entropy of t

### Moment and Balance

1. a = M3g/(M1+M2+M3) T = (M1+M2)M3g/(M1+M2+M3) M1 = 100, M2 = 150 and M3 = 1000 Kg What is a equal to and T equal to? 2. A non-uniform rod of mass 60g and a length 1 meter has a mass of 30g placed on one end and a mass of 40g placed on the other end. The rod together with the loads could be supported at a point 45cm from

### 5 Multiple Choice Problems on Simple Harmonic Motion (SHM) and Hooke's Law

1. A 300-g mass at the end of a spring oscillates with an amplitude of 7.0 cm and a frequency of 1.80 Hz. (a) Find its maximum speed and maximum acceleration. (b) What is its speed when it is 3.0 cm from its equilibrium position? A) 8.96 m/s, 8.9 m/s2 (b) 0.45 m/s B) 79.2 m/s, 895 m/s2 (b) 0.512 m/s C) 0.79 m/s, 8

### Elasticity: Stress, Strain and Compression

1. The figure below shows the forces acting on a tibia when a person stands on the ball of one foot in equilibrium. As shown, the force of the tibia on the ankle joint for a person (of weight 750 N) standing this way is 2800 N. The tibia has a length of 0.4 m, an average inner diameter of 1.3 cm, and an average outer diameter

### Torque, Equilibrium and Harmonic Motion

1. A uniform meterstick pivoted at its center has a 100 g mass suspended at the 25 cm position. (a) At what position should a 75 g mass be suspended to put the system in equilibrium? (b) What mass would have to be suspended at the 90 cm position for the system to be in equilibrium? 2. An organic pipe that is closed at one end

### Mechanics: Friction, Force, Incline, Equilibrium,

See attached file. Find the horizontal load P that will cause motion to the right, given coefficient of static friction for all surfaces is 0.33.

### Electrostatics and Oscillations: Oscillations in a Capacitor

A square parallel plate capacitor with vertical plates of area A and distance d, charged with a constant charge Q and is completely filled with a dielectric material the same dimension as the gap between the plates, with dielectric constant k and mass m. Assuming the dielectric is a solid block of material that can move inside t

### Magnitude and Direction of Third Force

An object in equilibrium has three forces exerted on it. A 33 N force acts at 90° from the x axis and a 46 N force acts at 60°. What are the magnitude and direction of the third force? ______N _________degrees (counterclockwise from the +x direction)

### Friction: Pushing a File Cabinet

You are pushing a filing cabinet across a rough floor (mk = 0.33) in a straight line at a constant speed. Which of the following statements about the magnitudes of the forces acting on the filing cabinet are correct? 1. true false if you exerted twice the force, the cabinet would accelerate across the floor. 2. true false

### Rotational equilibrium: Force and its moment (torque)

The figure shows a person whose weight is W = 644 N doing push-ups. Find the normal force exerted by the floor on (a)each hand and (b)each foot, assuming that the person holds this position.

### A cylinder hung at the end of two springs connected in series. To determine the maximum stretch.

A 7 kg cylinder is attached to a series of two springs - as shown in the attached illustration (see the attachment). If the cylinder is released from rest - when the springs are both un-stretched - determine the maximum stretch in each spring.

### Mechanics: Maximum stretch in spring holding block on incline

A 2.0 kg box rests on a plank that is inclined at an angle of 65° above the horizontal. The upper end of the box is attached to a spring with a force constant of 16 N/m, as shown in Figure 6-38. If the coefficient of static friction between the box and the plank is 0.28, what is the maximum amount the spring can be stretched an

### Tension in Pulley Systems

A winch is used to raise a 500 kg crate at a constant velocity (a = 0 m/s2). Determine the tension in the support arm and the angle theta. Note: the cable that runs from the motor, over the pulley, and to the 500 kg crate is continuous. The picture consists of a motor that has a cable running up to a pulley (which has the 500

### Tension Man Cart

A man is pulling a cart at 45 degrees pulling on cart with a string at 60 degrees find the tension ( find magnitude of the tension in the strap). Given info :is dimensions of cart, 2 angles, mass of cart center of gravity coincides with its geometrical center cart is moving.

### Application of Archimedes' Principle and Law of Flotation

A balloon filled with Helium and air is designed to support a mass of 106kg (payload+ empty balloon) and the mass of gases which fill it.Air density is 1.29kg/m^3, Helium plus air density in the balloon is 0.247kg/m^3, and Helium density is 0.179kg/m^3. Ignoring the volume of the payload, find the volume of the balloon. Answer i

### Buoyant Force, Projectile Range

A block of wood is held in water, totally immersed, by a string attached to a pont in the base of the tank. Calculation of range of jet stream flowing out of a tank. Please see the attachment.

### Rotational Equilibrium: Seesaw with Three Bodies

On the seesaw shown to the right (see attachment), mass A is 60 kg. mass B is 30 kg, and mass C is 10 kg. Mass A is 1.0m from the pivot. Mass C is 3.0m from the pivot. The see saw is at an angle of 30 degrees from the horizontal. Calculate the torques of mass A and mass C about the pivot. Where you should place mass B in relatio

### Simple Harminic Oscillation: Vertical Spring

A 100 gram weight is hung from a spring with a spring constant of 10 N/m. the position of the mass is measured from he equilibrium point. The mass is pulled down 10 cm and released at T=0. The position of the mass is given by x(t)=xcos(wt+theta). What are the values of all the constants in this equation? What is the maximum

### A bead of mass m slides without friction on a ring

A bead of mass m slides without friction on a ring. The ring rotates with constant angular velocity w about a rotational axis that is aligned with a ring diameter, as shown in Figure 1. Find the Lagrange equations of motion, and the Hamiltonian for the bead. Is the Hamiltonian a constant of motion? Does it coincide with the ener

### Friction: Conceptual Questions about Friction

Does kinetic friction depend on area? What about Normal force? or speed? And what is the difference between static and kinetic friction. Please help me understand kinetic friction.

### Energy, Angular Momentum, and Stable Equilibrium

Write down the equations of motion in polar coordinates for a particle of unit mass moving in a plane under a force with potential energy function V = -k ln r + cr + gr cos (theta), where K, c and g are positive constants. Find the positions or equilibrium (a) if c > g, and (b) if c < g. By considering the equations of motions n

### potential energy function

Please see the attached file. 7. A particle of mass m moves (in the region x >0) under a force F = -kx + c/x, where k and c are positive constants. Find the corresponding potential energy function. Determine the position of equilibrium, and the frequency of small oscillatoins about it.

### Three problems: Motion and equilibrium, Force, acceleration

16. The average speed of nitrogen molecule in air is about 6.70x10^2m/s, and its mass is 4.68x10^(-26) kg a) If it takes 3.00x10^-13s for a nitrogen molecule to hit a wall and rebound with the same speed but opposite direction, what is the average acceleration of the molecule during this time interval b)What average force do

### Electrostatics: Equilibrium due to two point charges.

Need help with this problem: Consider a positive point charge. i) Give an example of how you might place two other point charges so that the net force on the initial charge is zero. ii) If the net force on the charge is zero then this charge is in equilibrium. The equilibrium will be stable if, when the charge is displace

### Equilibrium of Bodies: Force and Tension

A body of mass 50 kg is suspended by two light, inextensible cables of lengths 15 m and 20 m from rigid supports placed 25 m apart on the same level. Find the tensions in the cables. Note that, by convention, "light" means "of negligible mass." Take g = 10 m/(s^2). This is an application using vector addition.

### Determining forces on two spheres hanging from a common point

Two small spheres with mass m= 15.6 g are hung by silk threads of length L= 1.18 m from a common point (see attachment). When the spheres are given equal charges, so that q1 = q2, each thread hangs at an angle theta= 25.0 degrees from the vertical. Draw a diagram showing the forces on the left sphere. Treat the spheres a

### angle of the rope with vertical

Please see the attached file. 1. a 50-lb box is suspended by a rope from the ceiling. If a horizontal force of 20 lb is applied to the box, what angle will the rope make with the vertical?

### Inclined Plane Calculations

1. A weight of 30lb rests on an inclined plane 3 ft high and 5 ft long. a force F making an angle of 30° with the plane pulls the body upward. If the coefficient of friction is 0.20, how much force is necessary to maintain uniform motion upward? 2. A board is 8 ft long. how high will one end be raised so that a block on it w