PHY 161 Exam 1 Review

tention

(cables, wires, ropes, etc - pulling)

Normal forces

(n) only when there is a support/contact from a surface-compressive

What forces act simultaneously on the same body, the resultant force will be greatest when the angle between them is...

0 degrees. (The resultant will always be greatest when vectors are parallel with one another (0 degrees) and point in the same direction).

A 25.0kg child sits on a rough incline of 30 degrees. Find the coefficient of static friction for the surface if the child is on the verge of slipping.

0.577 (You can automatically eliminate two choices a and d because the coefficient of friction is positive and a value of 13.9 is REALLY unphysical (you normally don't exceed 1 though some surfaces like rubber have values between 1-2). This is a Newton's 2nd Law problem but you would use AN INCLINED coordinate system (I have taken positive x to be DOWN the incline). Since you are looking at the case right before the child slips fs=usn

Two forces, A and B act simultaneously at point C. Both vectors have the same magnitude of 10N and act at right angles to one another. What is the closest estimate of their resultant?

14N (These two forces form a 45-45-90 right triangle, so the resultant has to be larger than 10N. This eliminates a because the answer cannot be 0 and d because it is too large to be physically reasonable

The Young's Modulus for steel is 2.0x10^11N/m^2. What is the stress experienced by a steel-rod that is 100cm long and 20 millimeters in diameter when it is stretched by a force of 6.3x10^3 N?

2.00x10^8 N/m^2 (Don't be fooled by this problem - half of the numbers given are totally unnecessary. This is a deformation problem and when yo are trying to find stress that means you are solving or pressure (as indicated by the units N/m^2=Pa). Since P=F/A, let us look at the force and the area. The force is 6.3x10^3N and the area is pir^2 (r=10mm) Therefore F/A=6.3x10^3N/pi(0.010m)^2=2x10^8N/m^2)

A body accelerates at 2.5m/s^2 when acted on by a net force of 5.0N. The mass of the body is...

2.0kg (Newton's second law is F=ma so m=Fa=5/2.5=2kg. You can also use physical/mathematical reasoning to eliminate some of the answers. The force is directly proportional to the acceleration, so it doesn't make sense to have a,b, or d.

A 100cm long steel rod experiences a stress of 4.0x10^8 N/m^2 when it is stretched by a force of 10N. The Young's Modulus of steel is 2.0x10^11 N/m^2. what is the strain on the rod?

2.0x10^-3 N/m^2. (The strain on the rod is known as deltaL/L so it is a number (no units since it is just the ratio of the change in the length to the original length.) That means we can automatically eliminate a and c. Since P=Young's Modulus strain, the strain is P/Young's Moduls.)

What is the magnitude and direction of vector B if Bx=-23.7m and By=15.5m?

28.3m and 147 degrees +x axis (There is no need for math to do this particular question. Since you have a negative x-component and a positive y-component, this means the vector must be in the second quadrant. Since the magnitude of the vector corresponds to the hypotenuse of the right triangle (where the components are the legs of the right triangle), this means the magnitude must be larger than either one of the legs. Therefore, the only correct answer is d.)

In the diagram shown, a box slides down an incline. Toward which point is the force of friction directed?

3 (Behind box). (Friction is a retarding force - it OPPOSES THE DIRECTION OF MOTION. So if the box is sliding down the incline, friction is pointing up the incline).

A cast iron cable is under 5000N of tension. What is the minimum radius of the cable to avoid snapping? Assume the cable is circular.

3.06x10^-3m (Please note the ultimate tensile strength of cast iron, 170x10^6 N/m^2 would be given on the equation sheet. Recall that stress is force/area, so that means that the ultimate tensile strength of the cast iron cable is equal to the tension/area and you can solve for the radius of the wire by re-writing the area as A=pir^2.

A rod with negligible mass is 10m in length. If a 30kg weight is suspended from one end of the rod and 20kg weight from the other, where must the pivot point be placed to ensure equilibrium?

4m from the 30kg weight. (This is an equilibrium/torque problem. Since the rod has negligible weight, you don't have to worry about torque from the rod's weight. That means only the two weights provide torques and since the rod is in equilibrium,the two torques have to be equal to one another. Suppose x is the distance from the 30kg weight, that means 10-x is the distance from the 20kg weight. This means that 30(x)=20(10-x) or that x=4m from the 30kg weight. So the answer is a. You could have done the problem using x as the distance from the 20kg weight and in that case, x=6m from the 20kg weight which is the same as 4m from the 30kg weight.

A 5.00 meter steel beam of uniform cross-section and composition weighs 100N. What is the minimum force required to lift one end of the beam?

50N (This is a torque problem. Because this is a uniform beam, all the weight is located at the center of beam at 2.5m. Since we are trying to lift the beam, the pivot point would be at the opposite end of the rod (5m). So in order for the force to lift the beam, it has to offset the torque from the weight of the beam. That means the torque from the weight of the beam (2.50m*100N) is equal amount of torque. That means F=50N).

A hiker travels 60 m North and 120 m South. What is her resultant displacement?

60 m South

A uniform ladder of 10.0m and weight of 100N makes an angle of 53 degrees with respect to a rough floor. If the ladder rests on a smooth wall, how far up the ladder can a 600N person climb before the ladder slips? The coefficient of friction is 0.355.

7.34m (By applying the strategies of mechanical equilibrium, you can solve this problem. Let us set the rotational origin/axis where the ground meets the ladder and take a standard x/y coordinate system with +x right and +y up. We then look at the forces acting on the ladder -fs pointing right and ng pointing up (both act the point where the ladder meets the ground); the weight of the ladder pointing straight down (acting at the physical center of the ladder); the weight of the person pointing straight down (acting some unknown part of the ladder); and nw pointing left at the point where the ladder meets the wall. We then write the conditions for mechanical equilibrium and begin to solve the problem.

A vector A makes an angle of 60 degrees with the x-axis of a Cartesian coordinate system (rectangular coordinate system). Which of the following statements is true?

Ay is greater than Ax. (You can automatically eliminate c and d because the resultant of a vector will NEVER be SMALLER than its components

Cart A has mass of 1 kg and a constant velocity of 3m/s. Cart B has a mass of 1.5kg and constant velocity of 2m/s. Which of the following statements is true?

Cart A has greater kinetic energy. (You can immediately eliminate answers c and d because both carts have constant velocities, so their accelerations are zero. Since KE=1/2mv^2, when you square Cart A's velocity, it is larger than Cart B's velocity, even though Cart B is more massive. The way to look at this is that the factor of increase in the mass (from A to B) is much less than the factor of decrease in the velocity (from A to B). So the larger velocity wins out.

What force is required to impart an acceleration of 10.0m/s^2 to a body with mass 2.0kg?

F=ma, so (2.00kg)(10.0m/s^2)=20.0N

Simple Harmonic Motion

How to determine position as a function of time using a sine or cosine function: x=Acos(2pift) or x=Asin(2pift) RADIAN MODE

Human occupancy within a home is considered...

Live load.

The primary purpose of buttressing is..

Neutralization of thrust at the bottom of a wall. (The main role of a buttress is to relay the horizontal thrust from the top of the building to the ground.)

A 50N chandelier is suspended by three cables as shown in the figure below. What is the tension in all three cables? (7)

T1=43N; T2=25N; T3=50N (There is no need for math to do this particular question. Since you have a negative x-component and a positive y-component, this means the vector must be in the second quadrant. Since the magnitude of the vector corresponds to the hypotenuse of the right triangle (where the components are the legs of the right triangle), this means the magnitude must be larger than either one of the legs). Only correct answer is d.

Resonance occurs when...

The frequency of an external vibration is equal to the natural frequency of the structure.

A chain suspended from two ends is an example of...

a catenary. (A chain suspended from its two ends is a freely hanging object that supports its own weight meaning it's a catenary.)

An arch is...

a means of spacing a space

Action reaction forces...

act on different objects always.

If a triangular arch has an asymmetric load placed on it,

an additional vertical force is needed at the top of the arch.(Whener the bridge weight is much, much heavier than the weight of the suspension cables, the shape of the bridge is parabolic.)

Kinetic friction

f>k or urn (friction opposes the direction of motion)

Stress=

force/area

After a rocket is launched, its engines shut off. The rocket continues to move in a straight line at a constant speed. This is an example of...

inertia. (This is Newton's 1st law. Inertia is the tendency to maintain the state of motion. You can also use the process of elimination for a- the object has a constant velocity so a=0, c- the object is in space so what is exerting any gravitational pull on it? d- action-reaction doesn't work because once the engines are turned off, there are no forces acting on the rocket - Newton's 2nd law is equal to zero here because the constant velocity means equilibrium.

Static friction

max value (Right before object slips it is fs or usn)

Weight =

mg (points straight down)

The majority of couplings fail due to...

shear. (The majority of couplings (in fact, the structures themselves) fail due to shear stress from lateral forces.)

The lowest voussoir in an arch is known as the...

springer. (The lowest voussoir in an arch (the one that touches the ground) is the springer.)

Which of the following are types of equilibrium?

stable, unstable, and neutral.

Many materials are...

stronger under compression than tension.

An object is balanced when it is...

supported at its center of gravity.

Trig identities are only relative...

to the angle that you choose.