Answer: B) 29.4 m/s^2
Explanation:
The g force is the gravitational force equivalent. Recall,
gravitational acceleration = 9.8m/s^2
This means that the 1 g force is equivalent to an acceleration of 9.8m/s^2
From the information given,
riders can experience a force of up to 3 g. Thus, the maximum acceleration of the roller coaster is
3 x 9.8
= 29.4
B) 29.4 m/s^2
How many seconds are required for the ranger’s vehicle in the previous problem to stop? Only enter the number not the units
Answer:
distance = 17.1 m
time = 3 s
Explanation:
First, we will use the following equation:
[tex]v^2_f=v^2_i+2a(\Delta x)[/tex]Where vf is the final velocity, vi is the initial velocity, a is the acceleration and
Δx is the distance. Then, replacing each value, we get:
[tex]\begin{gathered} 0^2=11.4^2+2(-3.8)(\Delta x) \\ 0=129.96-7.6\Delta x \end{gathered}[/tex]The final velocity is 0 m/s because the vehicle will come to rest and the acceleration is negative because it is slowing down.
Then, solving for Δx, we get:
[tex]\begin{gathered} 7.6\Delta x=129.96 \\ \frac{7.6\Delta x}{7.6}=\frac{129.96}{7.6} \\ \Delta x=17.1\text{ m} \end{gathered}[/tex]Now, with the distance and velocities, we can find the time t using the following equation:
[tex]\Delta x=\frac{1}{2}(v_i+v_f)t[/tex]So, replacing the values and solving for t, we get:
[tex]\begin{gathered} 17.1=\frac{1}{2}(11.4+0)t \\ 17.1=\frac{1}{2}(11.4)t \\ 17.1=5.7t \\ \frac{17.1}{5.7}=\frac{5.7t}{5.7} \\ 3\text{ s = t} \end{gathered}[/tex]Therefore, the answers are:
distance = 17.1 m
time = 3 s
If R1 < R2 < R3, and if these resistors are connected in parallel in a circuit, which one has the greatest voltage drop?
Since the resistors are in parallel, each one has the same voltage applied across their terminals.
The smaller the resistance of the resistor, the greater the current passing through it:
[tex]V=I\cdot R[/tex]But since all resistors have the same voltage, the voltage drop is the same for all three resistors.
Correct option: four
To estimate the maximum altitude reached by their rockets, the boys measured theO initial velocity of the rocketflight time of the rocketO internal diameter of the rocketO acceleration of gravity at the launch site
The maximum height of the rocket is determined as,
[tex]h=\frac{u^2\sin (\theta)}{2g}[/tex]where u is the initial velocity, g is the acceleration due to gravity and
[tex]\theta\text{ is the angle of the rocket initial velocity with the horizontal surface}[/tex]As the value of acceleration due to gravity is constant, thus, the height reached by rocket can be changed with the magnitude or the direction of the initial velocity of the rocket.
Hence, the first option (initial velocity of the rocket flight time of rocket) is the correct answer.
Ø = 23° and m = 108N. What is the tension T1 in Newton?
For this problem, we are going to need to balance forces out.
The sum of the forces in the y-direction and the sum of the forces in the x direction need to equal 0. The reason is, when we look at the diagram, there is no net force, which means the force of the object is 0.
Lets look at the forces in the y-direction
[tex]\Sigma F_y=F_g-F_1sin\theta[/tex]This equation is given when we balance the forces in the y-direction
Fg = mass * gravity = 108 N
If we plug this into the formula
[tex]\begin{gathered} \Sigma F_y=108-F_1sin\theta=0 \\ 108=F_1sin\theta \\ F_1=\frac{108}{sin23} \end{gathered}[/tex]When we solve for F1, we get 276.4 Newtons for tension in T1.
The average time it takes a pendulum to swing is 3.5 seconds. What absolute uncertainty must your measurement have to keep the relative uncertainty below 1%?
Given
The average time it takes a pendulum to swing is 3.5 seconds. What absolute uncertainty must your measurement have to keep the relative uncertainty below 1%?
Procedure
The relative uncertainty or relative error formula is used to calculate the uncertainty of a measurement compared to the size of the measurement. It is calculated as:
relative uncertainty = absolute error / measured value
3.5*1% = 0.035
3.5 +/- 0.035
The absolute uncertainty would be +/- 0.035
What is the intensity (in W/m2) of an electromagnetic wave with a peak electric field strength of 115 V/m?
Given:
The peak electric field strength is: E = 115 V/m
To find:
The intensity of an electromagnetic wave.
Explanation:
The intensity of an electromagnetic wave in terms of electric field intensity is given as:
[tex]I=\frac{c\epsilon_0E^2}{2}[/tex]Here, I = Intensity of an electromagnetic wave
c = The speed of light in a vacuum
ε₀ = The permittivity of free space
Standard data:
c = 3 × 10⁸ m/s
ε₀ = 8.854 × 10⁻¹² C²/N.m²
Substituting the values in the above equation, we get:
[tex]\begin{gathered} I=\frac{3\times10^8\text{ m/s}\times8.854\times10^{-12}\text{ C}^2\text{/N.m}^2\times115\text{ V/m}}{\text{ }2} \\ \\ I=17.56\text{ W/m}^2 \end{gathered}[/tex]Final answer:
The intensity of an electromagnetic wave is 17.56 W/m².
An inductor is connected to a 21.84 kHz oscillator. The peak current is 88.78 mA when the rms voltage is 58.62 V. What is the value of the inductance L, in millihenry's?
Let's name the variables we're given and that we know:
Vrms: rms voltage; Vrms = 58.62 V
ΔImax: maximum (peak) current; ΔImax = 88.78 mA = 88.78*10^-3 A
f: frequency; f = 21.84 kHz = 21.84*10^3 Hz
Now let's name some unknowns:
Irms: rms current
XL: inductive reactance
L: inductance
From equations and variables we know:
Irms = ΔImax/sqrt(2) = 88.78*10^-3/sqrt(2)
Irms = 0.063 A
XL = Vrms/Irms = 58.62/0.063
XL = 930.476 Ω
Finally,
L = XL/(2πf) = 930.476/(2π*21.84*10^3)
L = 0.00678 H = 6.78 mH
A plane is traveling at 150 m/s and accelerates at a rate of 6 m/s2 for 5 seconds and then continues on for 5 more seconds at this new velocity. Plot a velocity vs. time graph for the entire 10 seconds.
Given:
Velocity of the plane = 150 m/s
Acceleration for the first 5 seconds = 6 m/s²
If the plane continues on for 5 more seconds at this new velocity, let's plot a velocity vs time graph for the entire 10 seconds.
Let's first find the velocity for the second 5 seconds.
Apply the motion equation:
v = u + at
Where:
v is the final velocity
u is the initial velocity = 150 m/s
a is acceleration = 6 m/s²
t is the time = 5 seconds
• Velocity for the first 5 seconds:
v = 150 + 6×5
v =150 + 30
v = 180 m/s
The velocity for the first 5 seconds is 180 m/s
• To find the velocity for the next 5 seconds, we have:
v = u + at
Where:
u = 180 m/s
a = 6 m/s²
t = 5 seconds
Thus, we have:
v = 180 + 6×5
v = 180 + 30
v = 210 m/s
Thus, the velocity for the next 5 seconds is 210 m/s.
The velocity vs time graph for the entire 10 seconds is below:
Which property is a characteristic of single-slit diffraction but not double-slit diffraction?1) the central bright band2) bands are equally spaced3) bands get thinner farther from the band4) red light bands are spaced farther from each other than blue light bands
In the single slit diffraction, the bands get thinner farther from the band but this condition is not applicable in the case of the double slit diffraction.
As, the single slit diffraction has a central maxima and many smaller minima and maxima on the either side of the central maxima whose bands get thinner as distance from the central band is increased but not in the case of double slit diffraction due to the interference phenomenon.
Hence, option 3 (bands get thinner farther from the band) is the correct answer.
A slingshot has a spring constant of 550 N/m. A 40 gram pellet is placed in the slingshot and then drawn back 20 cm from equilibrium. If the pellet is released straight up, how far up will the pellet travel from its starting position?
28.06 metres
Explanation
Step 1
find the elastic potential energy
it is given by:
[tex]\begin{gathered} E_k=\frac{1}{2}kx^2 \\ \text{where kis the constant of the slingshot} \\ x\text{ is the distance} \end{gathered}[/tex]so
convert the measure into meteres and kg
[tex]\begin{gathered} 40\text{ gr =}\frac{\text{40}}{1000}kg\text{ = 0.040 }kg \\ 20cm=\text{ }\frac{\text{20}}{100}=0.2m \end{gathered}[/tex]so
[tex]\begin{gathered} E_k=\frac{1}{2}kx^2 \\ E_k=\frac{1}{2}\cdot550\frac{N}{m}\cdot(0.2)^2 \\ E_k=\frac{1}{2}\cdot550\frac{N}{m}\cdot(0.2)^2 \\ E_k=11\text{ J} \end{gathered}[/tex]Step 2
now, use the conservation of energy law to find the maximum heigth
[tex]\begin{gathered} \text{elastic energy = potential eneregy} \\ 11\text{ J = mgh} \\ so \\ h=\frac{11}{mg} \\ \text{replace} \\ h=\frac{11\text{ J}}{0.040kg\cdot9.8\frac{m}{s^2}} \\ h=28.06\text{ meters} \end{gathered}[/tex]therefore, the answer is
28.06 metres
I hope this helps you
A circuit with a 21 V battery a 10 Ω resistor and 15 Ω resistor in series. What is the current throughout the circuit?
Given data:
* The voltage across the battery is,
[tex]V=21\text{ volts}[/tex]* The value of resistances given is,
[tex]\begin{gathered} R_1=10\text{ ohm} \\ R_2=15\text{ ohm} \end{gathered}[/tex]Solution:
The equivalent resistance of the given resistors connected in series is,
[tex]\begin{gathered} R_{eq}=R_1+R_2 \\ R_{eq}=10+15 \\ R_{eq}=25\text{ ohm} \end{gathered}[/tex]According to Ohm's law, the current through the circuit is,
[tex]\begin{gathered} V=IR_{eq} \\ I=\frac{V}{R_{eq}} \\ I=\frac{21}{25} \\ I=0.84\text{ A} \end{gathered}[/tex]Thus, the current through the circuit is 0.84 A.
what type of energy would be gasoline?
Gasoline contains Chemical potential energy.
The energy is stored in the bonds of hydrocarbons (potential energy) , then it is released when ignited.
Hello! Is it possible to get help on this question, I do not understand why it was marked wrong
To find
Which of the following has units of velocity
Explanation
The unit of velocity is m/s
Conclusion
So the correct option are
-120 m/s
9.8m/s downward
To get up on the roof, a person (mass 80.0 kg) places a 5.40 m aluminum ladder (mass 13.0 kg) against the house on a concrete pad with the base of the ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to be frictionless. The center of mass of the ladder is 2 m from the bottom. The person is standing 3 m from the bottom. What are the magnitudes (in N) of the forces on the ladder at the top and bottom?TOP =BOTTON =
The given problem can be exemplified in the following diagram:
Where:
[tex]\begin{gathered} Ft=\text{ force at the top} \\ W_p=\text{ weight of the person} \\ W_l=\text{ weight of the ladder} \\ F_{by},F_{bx}=\text{ y and x components of the force at the bottom} \end{gathered}[/tex]To determine the value of the forces at the top and bottom we will first use the sum of moments with respect to point B. The moments in the counterclockwise direction will be considered to be positive.
The moments are:
[tex]\Sigma M_B=W_p(3\cos\theta)+W_l(2\cos\theta)-F_Th[/tex]Since the ladder is not turning this means that the sum of moments is zero, therefore, we have:
[tex]W_p(3\cos\theta)+W_l(2\cos\theta)-F_Th=0[/tex]Now, since the weight is the product of the mass and the acceleration of gravity we have:
[tex]m_pg(3\cos\theta)+m_lg(2\cos\theta)-F_Th=0[/tex]Where:
[tex]\begin{gathered} m_p=\text{ mass of the person} \\ m_l=\text{ mass of the ladder} \end{gathered}[/tex]We can use the right triangle formed by the ladder and the wall to determine the cosine of the angle theta, like this:
Since the cosine is defined as:
[tex]\cos\theta=\frac{adjacent}{hypotenuse}[/tex]Substituting we get:
[tex]\cos\theta=\frac{2}{5.4}[/tex]Now, we substitute the value of the cosine:
[tex]m_pg(3(\frac{2}{5.4}))+m_lg(2(\frac{2}{5.4}))-F_Th=0[/tex]To determine the value of "h" we apply the Pythagorean theorem to the right triangle:
[tex]2^2+h^2=5.4^2[/tex]Now, we solve the squares:
[tex]4+h^2=29.16[/tex]Now, we subtract 4 from both sides:
[tex]\begin{gathered} h^2=29.16-4 \\ h^2=25.16 \end{gathered}[/tex]Now, we take the square root to both sides:
[tex]h=\sqrt{25.16}[/tex][tex]h=5.02[/tex]Now, we substitute the values:
[tex](80kg)(9.8\frac{m}{s^2})(3m(\frac{2}{5.4}))+(13kg)(9.8\frac{m}{s^2})(2m(\frac{2}{5.4}))-F_T(5.02m)=0[/tex]Now, we solve the operations:
[tex]965.48Nm-F_t(5.02m)=0[/tex]Now, we solve for the force at the top. Adding Ft(5.302m) to both sides:
[tex]965.48Nm=F_t(5.02m)[/tex]Now, we divide both sides by 5.02m:
[tex]\frac{965.48Nm}{5.02m}=F_t[/tex]Solving the operations:
[tex]192.33N=F_t[/tex]Now, to determine the forces at the bottom we will use the sum of forces. For the x-component, we add the horizontal forces, like this:
[tex]\Sigma F_h=0[/tex]Adding the forces we get:
[tex]F_t+F_{bx}=0[/tex]Now, we subtract the force at the bottom from both sides:
[tex]F_{bx}=-F_t[/tex]Now, we substitute:
[tex]F_{bx}=-192.33N[/tex]Now, we add the vertical forces:
[tex]F_{by}-m_pg-m_lg=0[/tex]Now, we solve for the y-component:
[tex]F_{by}=m_pg+m_lg[/tex]Now, we plug in the values:
[tex]F_{by}=(80kg)(9.8\frac{m}{s^2})+(13kg)(9.8\frac{m}{s^2})[/tex]Solving the operations:
[tex]F_{by}=911.4N[/tex]Now, the magnitude of the bottom force is given by:
[tex]F_b=\sqrt{F_{bx}^2+F_{by}^2}[/tex]Substituting the values we get:
[tex]F_b=\sqrt{(-192.33N)^2+(911.4N)^2}[/tex]Solving the operations:
[tex]F_b=931.47N[/tex]Therefore, the bottom force is 931.47N
If several forces are exerted on a system, calculate the work done by each force, then multiply the results. Is this true or false?
If the numebr of forces acting on the system, then depending upon the direction of each force, the work done is calculated.
The net work done is not the muliplication of work done by the each force.
The net resultant force acting on the system is calculated and the resultant displacement of the system is calculated.
Then with the resultant force and displacement, the workdone on the system is obtained.
Hence, the given statement is false.
Using a force of 60N, how much work would you do in pushing a 150N piece of furniture 20m across the room?
Given,
The applied force, F=60 N
The weight of the furniture, W=150 N
The distance through which the furniture was pushed, d=20 m
The work done by the source is given by the product of the force applied by the source and the distance for which the force was applied.
Therefore the work done by you is given by,
[tex]W_d=F\times d[/tex]On substituting the known values,
[tex]\begin{gathered} W_d=60\times20 \\ =1200\text{ J} \end{gathered}[/tex]Therefore, the work done by you in moving the given piece of furniture is 1200 J
A spacecraft travels directly from Earth to the Moon. Where is the vector sum of the gravitational forces exerted on the spacecraft by Earth and by the Moon zero?
Gravitational force, F is directly proportional to the mass of the object.
The mass of the satellite is the same for both earth and the moon.
So, Gravitational force of earth > gravitational force of the moon
Also, the distance is inversely proportional to the gravitational force.
Thus, the vector sum of gravitational force due to earth and due to the moon on the satellite will be zero, when the satellite is more than halfway to the moon.
a bullet is fired horizontally with a speed of 524 m/s from a height of 22m above the ground. calculate where it will hit the ground
Given data:
* The height of the bullet is 22 m.
* The speed of bullet in the horizontal direction is 524 m/s.
Solution:
By the kinematics equation, the time taken by the bullet to reach the ground is,
[tex]h=u_yt+\frac{1}{2}gt^2[/tex]where u_y is the vertical velocity component, t is the time taken to reach the ground, g is the acceleration due to gravity, and h is the height of the bullet,
Substituting the known values,
[tex]\begin{gathered} 22=0+\frac{1}{2}\times9.8\times t^2 \\ t^2=\frac{22\times2}{9.8} \\ t^2=4.49 \\ t=2.12\text{ s} \end{gathered}[/tex]Thus, the time taken by the bullet to reach the ground is 2.12 seconds.
By the kinematics equation for the horizontal motion, the horizontal range of the bullet is,
[tex]R=u_xt+\frac{1}{2}at^2[/tex]where u_x is the horizontal component of the velocity, a is the acceleration along the horizontal direction, t is the time taken to reach the ground and R is the horizontal range,
Substituting the known values,
[tex]\begin{gathered} R=524\times2.12+0 \\ R=1110.9\text{ m} \end{gathered}[/tex]Thus, the horizontal range of the bullet is 1110.9 meters.
Hence, the bullet hit the ground at 1110.9 meters.
_____ are not valid units for the measurement of electric potential difference.1) V2) J/C3) N m/C4) C/J
The simple unit of the electrical potential difference is Volt.
In terms of the charge and potential energy, the unit of electric potential is J/C.
In terms of the force and displacement, the unit of electric potential is Nm/C.
As the J/C is the unit of electric potential, thus, it is not possible to have units of C/J for the electric potential difference.
Thus, C/J is not valid unit for electrical potential difference.
Hence, option 4 (C/J) is the correct answer.
Gavin doesn't like stepping on the cold stone floor of his room on winter mornings. He isusually careful to walk on the rugs laid over parts of the floor. One day, he wonders why the rugs feel warmer than the stone floor. Since the rugs sit on the bare floor all the time, he thinks they should be at about the same temperature.Which of the following is a good hypothesis Gavin can use to help satisfy his curiosity?A. What is the specific heat of carpet?B. Cold radiates out of the stone floor.C. Stone is a better thermal conductor than rugs.D. The stone floor feels colder than the carpet does.
In order to answer this question, let's go through all of the four options
A. What is the specific heat of carpet?
- This is not a good hypothesis because it is already posed as a question, not a feasible solution (what a hypothesis should be)
B. Cold radiates out of the stone floor.
- This is not a good hypothesis because it is hard to quantify this. The cold can radiate technically out of anything
C. Stone is a better thermal conductor than rugs.
- This is a good hypothesis because this statement can be tested and then proved false or correct.
D. The stone floor feels colder than the carpet does.
- This is not a good hypothesis since this is an opinion more than a statement
The correct answer is C
1. The distance between two corresponding parts of a wave is its A trough B frequency C wavelength D amplitude
Two corresponding parts of a wave could be crest -crest, trough - trough. The distance between these corresponding parts is called
wavelength
Calculate the total charge on a 25µF capacitor connected to a constant voltage of 100V in a d.c. circuit. How much energy is stored in the capacitor?
In order to calculate the charge storaged on the capacitor, use the following formula:
C = Q/V
where,
C: capacitance = 25µF = 25*10^-6F
Q: charge = ?
V: voltage = 100V
Solve the equation above for Q, replace the values of the other parameters and simplify:
[tex]Q=CV=(25\cdot10^{-6}F)(100V)=0.0025C_{}[/tex]Hence, the total charge on the capacitor is 0.0025C
Which of the following X-Y tables agrees withthe information in this problem?A runner moves 2.88 m/s north. She accelerates at0.350 m/s’ at a -52.0° angle. At the point in the motionwhere she is running directly east, how far is she fromher starting point?ХYB)XYC)хYA)ViVA2.88OV:O2.88V:oo2.88?V+0Via0.276 0.215a-0.276a0.350-0.3500.215PAx?- ?AX?Axt0ott
Given, initial velocity in the y-direction, vi=2.88 m/s
The acceleration of the runner, a=0.350 m/s²
The angle at which she is running, θ=-52.0°
The x-component of the acceleration is
[tex]a_x=a\times\cos \theta[/tex]On substituting the known values,
[tex]a_x=0.350\times\cos -52.0^0=0.215m/s^2[/tex]And the y-component of the acceleration is,
[tex]a_y=a\times\sin \theta[/tex]On substituting the known values,
[tex]a_y=0.350\times\sin (-52.0)=-0.276m/s^2[/tex]We can see that only table B has these values.
Therefore the correct answer is option B
[6.01] What is the first step to solving the system by eliminatingthe y variable first?4x − 5y = 43x + 2y = −20
ANSWER:
x = -4 and y = -4
STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} 4x-5y=4 \\ 3x+2y=-20 \end{gathered}[/tex]We solve by elimination:
To eliminate the variable y first, we multiply the first equation by 2 and the second equation by 5, just like this:
[tex]\begin{gathered} 2\cdot(4x-5y)=2\cdot4\rightarrow8x-10y=8 \\ 5\cdot(3x+2y)=5\cdot-20\rightarrow15x+10y=-100 \\ \text{ now, we add the equations:} \\ 8x-10y+15x+10y=8-100 \\ 23x=-92 \\ x=-\frac{92}{23} \\ x=-4 \\ \text{solve for y:} \\ -4\cdot-4-5y=4 \\ -5y=4+16 \\ y=\frac{20}{-5} \\ y=-4 \end{gathered}[/tex]what is the total mechanical energy of a 73 kg cyclist on a 8 kg bicycle half way down a 40 m hulk traveling a 10 m/sec
Given data
*The given mass of the cyclist is m = 73 kg
*The given mass of the bicycle is M = 8 kg
*The bicycle travels halfway down at a height is h = 20 m
*The hulk is traveling at a speed is v = 10 m/s
The expression for the total mechanical energy is given as
[tex]\begin{gathered} U_m=U_k+U_p \\ =\frac{1}{2}(m+M)v^2+(m+M)gh \end{gathered}[/tex]*Here g is the acceleration due to the gravity
Substitute the known values in the above expression as
[tex]\begin{gathered} U_m=\frac{1}{2}(73+8)(10)^2+(73+8)(9.8)(20) \\ =19926\text{ J} \end{gathered}[/tex]Hence, the total mechanical energy is U_m = 19926 J
Starting from rest, a(n)9 kg block slides 11 mdown a frictionless ramp (inclined at 30◦fromthe floor) to the bottom. The block thenslides an additional 20.8 m along the floorbefore coming to stop.The acceleration of gravity is 9.8 m/sFind the speed of the block at the bottomof the ramp.Answer in units of m/s.018 (part 2 of 3) 10.0 pointsFind the coefficient of kinetic friction betweenblock and floor.019 (part 3 of 3) 10.0 pointsFind the magnitude of the mechanical energylost due to friction.Answer in units of J.
Given that the mass of the block is m = 9 kg.
The length of the ramp is d= 11 m.
The angle is 30 degrees.
Also, the initial speed of the block is u = 0.
The acceleration due to gravity is g =9.8 m/s^2
After moving down the ramp the block moves an additional distance d' = 20.8 m.
We have to find the speed of the block.
The speed can be calculated by the formula
[tex]\begin{gathered} v=\sqrt[]{2gd} \\ =\sqrt[]{2\times9.8\times11} \\ =14.68\text{ m/s} \end{gathered}[/tex]The coefficient of kinetic friction is
[tex]\begin{gathered} \mu=\tan 30^{\circ} \\ =0.577\text{ } \end{gathered}[/tex]Calculate the volume occupied by 1 mol of gas at 0°C and 1 atm.
Given:
Number of moles, n = 1 mol
Temperature, T = 0°C
Pressure, P = 1 atm
Let's find the volume.
To find the volume apply the ideal gas law:
[tex]PV=nRT[/tex]Where:
• P is the pressure = 1 atm
,• T is the temperature in kelvin = 0°C + 273 = 273 K
,• n is the number of moles = 1 mol
,• R is the universal gas constant = 0.08206 L.atm/mol.K
,• V is the Volume.
Rewrite the formula for V:
[tex]V=\frac{nRT}{P}[/tex]Substitute the values into the formula and solve for V:
[tex]\begin{gathered} V=\frac{1*0.08206*273}{1} \\ \\ V=22.4\text{ L} \end{gathered}[/tex]Therefore, the volume is 22.4 L
ANSWER:
22.4 L
Electron Charge) You rub a balloon against your hair. The balloon gains a charge of -4.0µC. What charge does your hair have now?
Given
After rubbing the balloon against the hair, the balloon gains a charge of
[tex]-4.0\mu C[/tex]To find'
The charge the hair have
Explanation
We know charge is conserved.
So the hair would have charge
[tex]+4.0\mu C[/tex]Conclusion
The charge in the hair is
[tex]+4.0\mu C[/tex]A clown in a circus acts swings a 2.7 kg Metal ball attached to a 72 cm nylon string in a horizontal circle above her head making one revolution in 0.98 seconds what is the tension force exerted on the string of the ball
ANSWER:
80 N
STEP-BY-STEP EXPLANATION:
The tension in the string in this case would be the resultant force that exists in the string due to the centripetal effect of the swinging ball, that is, it is equal to the centripetal force.
We calculate the centripetal force as follows:
[tex]\begin{gathered} F_c=\frac{mv^2}{r} \\ T=\frac{mv^2}{r} \end{gathered}[/tex]Linear velocity is equal to the angular velocity of the ball multiplied by the radius of the ball:
We substitute the velocity to calculate the tension:
[tex]\begin{gathered} T=\frac{2.7\cdot4.62^2}{0.72} \\ T=80.04\cong80\text{ N} \end{gathered}[/tex]The tension is 80 N
A person driving a car suddenly applies the brakes. The car takes four seconds to come to rest while traveling 20 m at constant acceleration.Can the speed of the car immediately before the brakes are applied be determined without first determining the car’s acceleration?a. Yes, by dividing the distance (20m) by the time (4s).b. Yes, by determining the average speed while braking and doubling it. c. No, because the acceleration is needed to use equations such as change in position=initial velocity + 1/2 acceleration • time^2d. No, because the fundamental relationship that defines velocity contains acceleration. Explain why choice A is wrong.Explain why the correct choice is correct. Use words like “average speed (or velocity)”, “initial speed (or velocity)”, “final speed (or velocity)”, “total distance”, and “total time.” Refer to appropriate basic motion equations.
ANSWER:
b. Yes, by determining the average speed while braking and doubling it.
STEP-BY-STEP EXPLANATION:
Option A is not correct because both speeds, the final and the initial, are not taken into account.
To determine the correct answer, the first thing to do is to do it mathematically. Just like this:
[tex]\begin{gathered} v=u+at\rightarrow a=\frac{v-u}{t} \\ \\ s=ut+\frac{1}{2}at^2 \end{gathered}[/tex]We replacing
[tex]\begin{gathered} s=ut+\frac{1}{2}(\frac{v-u}{t})t^2 \\ \\ s=ut+\frac{1}{2}vt-\frac{1}{2}ut \\ \\ s=\frac{1}{2}t(u+v) \\ \\ v=0 \\ \\ s=\frac{1}{2}tu\rightarrow u=\frac{2s}{t} \end{gathered}[/tex]The average speed, that is, the average between the initial speed and the final speed, is determined since the final speed is 0, because it ends up braking. We can calculate the initial start since we know the total braking time (4 seconds) and the total distance we also know to be 20 meters, using the previous equations.
Therefore, the correct answer is: b. Yes, by determining the average speed while braking and doubling it.