#### Miscellaneous Physics Problems

FOR QUESTIONS 1-20 CHOOSE THE RIGHT ANSWER AND CIRCLE THE LETTER CORRESPONDING TO THE ANSWER 1) A slice of bread is squeezed into a little ball, which quantity does not change. A Mass B Volume C Density D Width 2) A boy measured the height of a laboratory table wi...

#### Lagrangian of Three Masses and Two Springs

Three identical masses m are connected to 2 identical springs of stiffness k and equilibrium length b, as shown in the figure above. The masses are free to oscillate in one dimension along an axis that runs through all three. They lie on a level, frictionless, horizontal surface. Introduce coordinat...

#### Variable Refractive Index

Light is passing through a 4 cm thick slab of special doped glass. The index of refraction varies smoothly n=2/sqrt(h) where "h" is the distance from one surface of the slab measured in centimeters. Use Fermat's principle to find the equation for the path of a light ray going from the high index sid...

#### Damped Forced Oscillations

A single stage vibration isolation system consists of a heavy granite slab (100 kg) sitting on legs which act as a vertical damped spring. The "Q" (Quality Factor) of the system is 8.0, and the velocity damping coefficient is 80 kg/s. What is the natural frequency of oscillation of the slab? Write d...

#### Determining a value from a slope

If the mass density of the string is 0.0013 kg/m and measurement of the relevant length of the string is 1.36 m and the slope, k, of the graph is 1,000 s^-2 kg^-1, then what is the measured value for the acceleration due to gravity, g? Include units. The problem and equation are attached as a pdf...

#### Tilted Rigid Disk Rolling Without Slipping

The figure is attached as file. A rigid body in the shape of a thumbtack formed from a thin disk of mass M and radius a and a mass-less stem is placed on an inclined plane that makes an angle α with the horizontal. The point of the tack remains stationary at the point α, and the head rolls alo...

#### Normal modes of a composite string

Consider the normal modes of a vibration under uniform tension of a stretched string consisting of two sections of unequal mass density, so that the wave speed differs from one section to the next. a. What conditions must be satisfied by the string displacement at the junction of the two sections...

#### Binary and decimal system

1. Convert the following decimal numbers to binary a. 81_10 b. 248_10 2. Convert the following octal numbers to binary a. 47_8 b. 214_8 3. Convert the following hexadecimal numbers tobinary a. BA3_16 b. F3B4_16 4. Convert the following binary nu...

#### Calculating Static Friction

A box of mass 80 kg is lying on a horizontal floor. The coefficient of static friction between the box and the floor is 0.6. Calculate the minimum force F required to pull it. Take g as 9.8 m.s^2. Refer the diagram. State minimum F in Newton. See attached file for diagram.

#### Magnification and Distance Calculations

Please see the attached file. SOD is source to object distance and SID is source to image distance. 1. With reference to Fig. 1(a) show that the magnification of an object is given by M = SID/SOD b. With reference to Fig. 1(b) show that the size of the penumbra (blur) f is given by f = Fx (M-1)...

#### Gas Mileage and Milliliter Obtainability

a) If an automobile is able to travel 254 miles on 11.2 gallons of gasoline, what is the gas mileage in km/L? b) A pound of coffee yields 50 cups of coffee (4 cups = 1 qt). How many milliliters of coffee can be obtained from 1 g of coffee beans? Please provide a detailed explanation.

#### Classical Mechanics of Displacement

1. Starting with the left-most column, populate the boxes from left to right without skipping empty boxes. Ties should be grouped in the same box. Rank the magnitude of a given particle's average acceleration, from smallest to largest, as interpreted from the following velocity vs. time graphs descr...

#### Mass and Pivot Points Problem

A boy and a girl are balanced on a massless seesaw. The boy has a mass of 75 kg and the girl's mass is 50 kg. If the boy sits 2.0 m from the pivot point on one side of the seesaw, where must the girl sit on the other side?

#### Problem 3-29

Beverly Mills has decided to lease a hybrid car to save on gasoline expenses and to do her part to help keep the environment clean. The car she selected is available from only one dealer in the local area, but that dealer has several leasing options to accommodate a variety of driving patterns. All ...

#### The Pressure on A2 in PSI

Two pistons push down on the fluid filling two cylinders connected by a narrow hose, as shown in the figure. The area A1 is 1 square inch, and the area A2 is 10 square inches. A force of 4 pounds is exerted downward on piston 1, as shown. Complete the following on the basis of this information. The...

#### Minimum Deceleration Time of Locomotive

An engineer in a locomotive sees a car stuck on the track at a railroad crossing in front of the train. When the engineer first sees the car, the locomotive is 130 m from the crossing and its speed is 17 m/s. If the engineer's reaction time is 0.36 s, what should be the magnitude of the minimum ...