Explanation:
It is given that,
Mass of golf club, m₁ = 210 g = 0.21 kg
Initial velocity of golf club, u₁ = 56 m/s
Mass of another golf ball which is at rest, m₂ = 46 g = 0.046 kg
After the collision, the club head travels (in the same direction) at 42 m/s. We need to find the speed of the golf ball just after impact. Let it is v.
Initial momentum of golf ball, [tex]p_i=m_1u_1=0.21\ kg\times 56\ m/s=11.76\ kg-m/s[/tex]
After the collision, final momentum [tex]p_f=0.21\ kg\times 42\ m/s+0.046v[/tex]
Using the conservation of momentum as :
[tex]p_i=p_f[/tex]
[tex]11.76\ kg-m/s=0.21\ kg\times 42\ m/s+0.046v[/tex]
v = 63.91 m/s
So, the speed of the golf ball just after impact is 63.91 m/s. Hence, this is the required solution.
A red ball of mass 5.57 kg is suspended between two walls on a string, as illustrated here. The weight of the ball causes the string to sag, making an angle \theta=θ= 19.4 degrees as indicated. What is the resulting tension F T T in the string, in Newtons?
Answer:
164.33 N
Explanation:
Given:
The mass of the ball, m = 5.57 kg
Angle made by the sag = 19.4°
it is required to find the tension [tex]F_T[/tex] in the string
Note: Refer the attached figure
The tension in the string will be caused by the weight of the wall
thus,
Weight of the ball, W = 5.57 kg × 9.8 m/s² = 54.586 N
Now the resolving the tension [tex]F_T[/tex] in the string into components as shown in the figure attached, the weight of the ball will be balanced by the sin component of the tension
thus,
W = [tex]F_T[/tex]sinΘ
or
54.586 N = [tex]F_T[/tex] sin 19.4°
or
[tex]F_T[/tex] = 164.33 N
Hence, the tension in the string will be 164.33 N
Determine explicitly which is faster, 75 miles per hour or 75 m/s? Express all your results in MKS units and explain your conclusions from the numbers, and explain using words. Show all work.
Answer:
75 m/s is faster
Explanation:
MKS units stands for meter kilogram seconds
75 miles per hour = 75 mph
1 mile = 1609.34 meters
1 hour = 60×60 = 3600 seconds
1 mph = 1609.34/3600 = 0.44704 m/s
75 mph = 75×0.44707 = 33.52792 m/s
Comparing 75 mph = 33.52792 m/s with 75 m/s it can be seen that 75 m/s is faster. Even without calculating the values you can know the answer. 75 mph means that in 1 hour the object will move 75 miles. 75 m/s means that in one second the object will cover 75 meters multiply by 3600 and you will get 270000 m/h that is 270 km/h divide it by 1.6 and you can approximately get the value in mph that will be around 168 mph which is faster than 75 mph.
A 64.0 kg skater moving initially at 2.81 m/s on rough horizontal ice comes to rest uniformly in 3.93 s due to friction from the ice. What force does friction exert on the skater?
Answer:
Force of friction, F = 45.76 N
Explanation:
t is given that,
Mass of the skater, m = 64 kg
Initial velocity of the skater, u = 2.81 m/s
Finally it comes to rest, v = 0
Time, t = 3.93 s
We need to find the force of friction. According to seconds law of motion as :
F = m × a
[tex]F=m\times \dfrac{v-u}{t}[/tex]
[tex]F=64\ kg\times \dfrac{0-2.81\ m/s}{3.93\ s}[/tex]
F = −45.76 N
So, the frictional force exerting on the skater is 45.76 N. Hence, this is the required solution.
A water pump draws about 9 A when connected to 240 V. What is the cost (with electrical energy at 13 cents per kWh) of running the pump for 16 h? (Give your answer in dollars)
Answer:
4.49 dollars
Explanation:
i = 9 A, V = 240 V, t = 16 h
Energy = V x i x t = 240 x 9 x 16 = 34560 W h = 34.56 kWh
The cost of 1 kWh is 13 cents.
Cost of 34.56 kWh = 13 x 34.56 = 449.28 cents = 449.28 / 100 = 4.49 dollars
The cost of running a water pump drawing 9 A at 240 V for 16 hours, with an energy cost of 13 cents per kWh, is $4.49.
Explanation:To calculate the cost of running a water pump for 16 hours at an electrical energy cost of 13 cents per kWh, you need to follow these steps:
First, calculate the power consumed by the pump. Power (P) is given by the formula P = VI, where V is the voltage and I is the current. For a pump drawing 9 A at 240 V, the power consumed is P = 240V * 9A = 2160W or 2.16kW.Next, calculate the total energy consumed in kilowatt-hours. Energy (E) is calculated as E = Pt, where P is the power in kW and t is the time in hours. For 16 hours, the energy consumed is E = 2.16kW * 16h = 34.56kWh.Finally, calculate the cost by multiplying the total energy consumed by the cost per kilowatt-hour. The cost (C) is C = E * cost/kWh. So, the cost to run the pump for 16 hours is C = 34.56kWh * $0.13/kWh = $4.4928.In dollars, the cost of running the pump for 16 hours is $4.49 (rounded to the nearest cent).
A piece of iron block moves across a rough horizontal surface before coming to rest. The mass of the block is 3.3 kg, and its initial speed is 3.2 m/s. How much does the block's temperature increase, if it absorbs 74% of its initial kinetic energy as internal energy? The specific heat of iron is 452 J/(kg · °C).
°C
Answer:
Rise in temperature is given as
[tex]\Delta T = 8.4 \times 10^{-3} ^0C[/tex]
Explanation:
Initial kinetic energy of the block is given as
[tex]KE = \frac{1}{2}mv^2[/tex]
here we will have
m = 3.3 kg
v = 3.2 m/s
now we will have
[tex]KE = \frac{1}{2}mv^2[/tex]
now we will have
[tex]KE = \frac{1}{2}(3.3)(3.2)^2[/tex]
[tex]KE = 17 J[/tex]
now we know that 74% of initial kinetic energy is absorbed as internal energy of the block
so the rise in temperature of the block is given as
[tex]KE = ms\Delta T[/tex]
[tex]0.74 \times 17 J = (3.3)(452)\Delta T[/tex]
[tex]12.5 = 1491.6 \Delta T[/tex]
[tex]\Delta T = 8.4 \times 10^{-3} ^0C[/tex]
Answer:
The temperature increases 0.0084ºC
Explanation:
Please look at the solution in the attached Word file.
A coil has a resistance of 5Ω and an inductance of 100 mH . At a particular instant in time after a battery is connected across the coil, the current is 2 A, and is increasing at a rate of 20A/s a) What is the voltage of the battery. b) What is the time-constant of the circuit. c) What is the final value of the current. d) Plot I() Vs time.
I have seen this question before and the correct answer would be B
Hope this helped!!
Answer:
The correct answer would be B
Explanation:
A 79-kg worker at the Burj Khalifa, the tallest building in the world with its roof 828 m above the ground below, rides a series of elevators from the ground level to the roof. What is the worker's change in gravitational potential energy?
Answer:
Worker's change in gravitational potential energy = 641.69 kJ
Explanation:
Potential energy = Mass x Acceleration due to gravity x Height
PE = mgh
Mass, m = 79 kg
Acceleration due to gravity, g = 9.81 m/s²
Height, h = 828 m
Potential energy, PE = 79 x 9.81 x 828 = 641691.72 J = 641.69 kJ
Worker's change in gravitational potential energy = 641.69 kJ
A DVD drive is spinning at 100.0 rpm. A dime (2.00 gm) is placed 3.00 cm from the center of the DVD. What must the coefficient of friction be to keep the dime on the disk?
Answer:
0.3375
Explanation:
w = angular speed of the DVD drive = 100.0 rpm = [tex]100.0 \frac{rev}{min}\frac{2\pi rad}{1 rev}\frac{1 min}{60 sec}[/tex] = [tex]10.5\frac{rad}{sec}[/tex]
m = mass of the dime = 2 g = 0.002 kg
r = radius = 3 cm = 0.03 m
μ = Coefficient of friction
The frictional force provides the necessary centripetal force to move in circle. hence
frictional force = centripetal force
μ mg = m r w²
μ g = r w²
μ (9.8) = (0.03) (10.5)²
μ = 0.3375
A place kicker applies an average force of 2400 N to a football of .040 kg. The force is applied at an angle of 20.0 degrees from the horizontal. Contact time is .010 sec. a. Find the velocity of the ball upon leaving the foot. b. Assuming no air resistance find the time to reach the goal posts 40.0 m away. c. The posts are 4.00 m high. Is the kick good? By how much?
Answer:
a) The velocity of the ball upon leaving the foot = 600 m/s
b) Time to reach the goal posts 40.0 m away = 0.07 seconds
c) The kick won't e going inside goal post, it is higher by 10.34m.
Explanation:
a) Rate of change of momentum = Force
[tex]\frac{\texttt{Final momentum - Initial momentum}}{\texttt{Time}}=\texttt{Force}\\\\\frac{0.040v-0.040\times 0}{0.010}=2400\\\\v=600m/s[/tex]
The velocity of the ball upon leaving the foot = 600 m/s
b) Horizontal velocity = 600 cos20 = 563.82 m/s
Horizontal displacement = 40 m
Time
[tex]t=\frac{40}{563.82}=0.07s[/tex]
Time to reach the goal posts 40.0 m away = 0.07 seconds
c) Vertical velocity = 600 sin20 = 205.21 m/s
Time to reach the goal posts 40.0 m away = 0.07 seconds
Acceleration = -9.81m/s²
Substituting in s = ut + 0.5at²
s = 205.21 x 0.07 - 0.5 x 9.81 x 0.07²= 14.34 m
Height of ball = 14.34 m
Height of post = 4 m
Difference in height = 14.34 - 4 = 10.34 m
The kick won't e going inside goal post, it is higher by 10.34m.
A system is initially at conditions of
P= 200 kPa and V= 0.1 m^3
Heat is now added to the system, and the system expands in a constant pressure process. At the end of the process the volume has doubled.
(a) Calculate the work transferred during the process.
(b) During the process the internal energy of the system increases by 200 kJ; kinetic and potential energy remains constant. Determine the net heat transfer during the process.
Answer:
a)W=20 KJ
b) ΔQ= 220 KJ
Explanation:
Given:
V₁=0.1 m^3, P₁=200 kPa and heat is added to the system such that system expands under constant pressure.
Therefore V₂= 2V₁= 0.2 m^3
a) Work transfer W= P(V₂-V₁)= [tex]200\times(0.2-0.1)\times10^{5} = 2\times10^4 joules[/tex]
W=20 KJ
b) internal energy change ΔU= 200 KJ
from first law we know that ΔQ(net heat transfer)= ΔU + W
ΔQ= [tex]200\times10^3 +2\times10^4[/tex]
ΔQ=[tex]22\times10^4 J[/tex]
ΔQ= 220 KJ
An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner's 2.00 T field with his fingers pointing in the direction of the field. His wedding ring has a diameter of 2.5 cm and it takes 0.45 s to move it into the field. What average current is induced in the ring in A if its resistance is 0.0100 Ω ?
The average induced current in the loop is 0.218 A.
Induced emf in the loopThe emf induced in the loop is determined by applying Faraday's law as shown below;
emf = dФ/dt
emf = BA/t
where;
A is the area
A = πr² = πd²/4
A = π x (0.025)²/4
A = 4.908 x 10⁻³ m²
emf = (2 x 4.908 x 10⁻³)/(0.45)
emf = 2.18 x 10⁻³ V
Average induced currentThe average induced current in the loop is calculated as follows;
I = emf/R
I = 2.18 x 10⁻³/0.01
I = 0.218 A
Learn more about induced emf here: https://brainly.com/question/13744192
The Sun radiates electromagnetic energy at the rate of 3.92 × 1026 W. The mass of the Sun is 1.99 × 1030 kg. What fraction of the Sun’s mass is lost during a human lifetime of 75 years? A. 2.16 × 10–13 B. 1.42 × 10–14 C. 6.90 × 10–14 D. 5.18 × 10–12 E. 8.63 × 10
Answer:
D. 5.18 x 10⁻¹²
Explanation:
[tex]\frac{dE}{dt}[/tex] = rate at which sun radiates energy = 3.92 x 10²⁶ W
M = mass of sun = 1.99 x 10³⁰ kg
[tex]\frac{dm}{dt}[/tex] = rate at which sun's mass is lost
c = speed of light
Energy is given as
E = m c²
Taking derivative both side relative to "t"
[tex]\frac{dE}{dt}=c^{2}\frac{dm}{dt}[/tex]
[tex]3.92\times 10^{26}=(3\times 10^{8})^{2}\frac{dm}{dt}[/tex]
[tex]\frac{dm}{dt}[/tex] = 4.4 x 10⁹ kg/s
t = time interval = 75 yrs = 75 x 365 days = 75 x 365 x 24 hours = 75 x 365 x 24 x 3600 sec = 2.4 x 10⁹ sec
[tex]m[/tex] = mass lost
mass lost is given as
[tex]m = t\frac{dm}{dt}[/tex]
[tex]m = (2.4\times 10^{9})(4.4\times 10^{9})[/tex]
m = 10.56 x 10¹⁸ kg
fraction is given as
fraction = [tex]\frac{m}{M}[/tex]
fraction = [tex]\frac{10.56\times 10^{18}}{1.99\times 10^{30}}[/tex]
fraction = 5.18 x 10⁻¹²
A mass of 2.82 kg is hung from a spring, causing the spring to stretch 0.331 m. If a second mass of 3.09 kg is now added to the spring, how far with it now stretch with both masses hanging?? State your answer to the correct number of significant digits and include the proper units.
Answer:
0.694 m
Explanation:
Case 1 : When only mass of 2.82 kg is hanged from spring
m = mass hanged from the spring = 2.82 kg
x = stretch caused in the spring = 0.331 m
k = spring constant
Using equilibrium of force in vertical direction
Spring force = weight of the mass
k x = m g
k (0.331) = (2.82) (9.8)
k = 83.5 N/m
Case 2 : When both masses are hanged from spring
m = mass hanged from the spring = 3.09 + 2.82 = 5.91 kg
x = stretch caused in the spring = ?
k = spring constant = 83.5 N/m
Using equilibrium of force in vertical direction
Spring force = weight of the mass
k x = m g
(83.5) x = (5.91) (9.8)
x = 0.694 m
A football player at practice pushes a 60 kg blocking sled across the field at a constant speed. The coefficient of kinetic friction between the grass and the sled is 0.30. How much force must he apply to the sled?
180N
Explanation:Using Newton's law of motion;
∑F = m x a --------------------(i)
Where;
∑F = Resultant force
m = mass of the object (sled in this case)
a = acceleration of the sled
Calculate the resultant force;
Since the direction of motion is horizontal, the horizontal forces acting on the sled are the;
i. Applied force ([tex]F_{A}[/tex]) in one direction and;
ii. Frictional force ([tex]F_{R}[/tex]) in the other direction to oppose motion
Therefore, the resultant force ∑F is the vector sum of the two forces. i.e;
∑F = [tex]F_{A}[/tex] - [tex]F_{R}[/tex] -----------------------(i)
Frictional force [tex]F_{R}[/tex] is the product of the coefficient of kinetic friction (μ) and weight(W) of the sled. i.e
[tex]F_{R}[/tex] = μ x W
Where;
W = mass(m) x gravity(g)
W = m x g
=> [tex]F_{R}[/tex] = μmg
Substitute [tex]F_{R}[/tex] into equation (ii)
∑F = [tex]F_{A}[/tex] - μmg
Substitute ∑F into equation (i)
[tex]F_{A}[/tex] - μmg = ma -------------------(iii)
Since the motion is at constant speed, it means acceleration is zero (0)
Substitute a = 0 into equation (iii) to give;
[tex]F_{A}[/tex] - μmg = 0
=> [tex]F_{A}[/tex] = μmg
Substitute the values of μ = 0.3, m = 60kg and g = 10m/s² into the above equation to give;
=> [tex]F_{A}[/tex] = 0.3 x 60 x 10
=> [tex]F_{A}[/tex] = 180N
This means that the applied force should be 180N
The amount of force the football player must apply to the sled is 176.4 Newton.
Given the following data:
Mass of sled = 60 kgCoefficient of kinetic friction = 0.30We know that acceleration due to gravity (g) on Earth is equal to 9.8 [tex]m/s^2[/tex]
To find how much force the football player must apply to the sled:
Mathematically, the force of kinetic friction is given by the formula;
[tex]Fk = umg[/tex]
Where;
Fk represents the force of kinetic friction.μ represents the coefficient of friction.m represents the mass.g is the acceleration due to gravity.Substituting the given parameters into the formula, we have;
[tex]Fk = 0.30\times60\times9.8[/tex]
Force, Fk = 176.4 Newton.
Read more: https://brainly.com/question/13754413
What is your weight on Venus, assuming that the acceleration due to gravity on Venus is 8.875 m/s^2 and your mass is 50 kg.
Answer:
Weight on Venus = 443.75 N
Explanation:
Weight of a body is the product of mass and acceleration due to gravity.
So we have
Weight = Mass x Acceleration due to gravity
W = mg
Mass, m = 50 kg
Acceleration due to gravity, g = 8.875 m/s²
W = 50 x 8.875 = 443.75 N
Weight on Venus = 443.75 N
Answer:
443.75 N
Explanation:
Weight is the force with which a planet can attract anybody towards its centre.
Weight = mass of body × acceleration due to gravity on that planet
Weight = 50 × 8.875 = 443.75 N
Two man pull on a cart with a mass of 90 kg. if 1 man pulls 140 N to the right and the other man pulls 195 N to the left then find the magnitude and direction of the acceleration for the cart
Answer:
magnitude : 0.6 m/s²
Direction : Left
Explanation:
m = mass of the cart = 90 kg
Taking force in right direction as positive and force in left direction as negative
F₁ = Force applied by man 1 = 140 N
F₂ = Force applied by other man = - 195 N
a = acceleration of the cart
Force equation for the motion of the cart is given as
F₁ + F₂ = ma
140 + (- 195) = 90 a
a = - 0.6 m/s²
magnitude of acceleration is 0.6 m/s²
The negative sign indicates the direction of acceleration towards left
Final answer:
The magnitude of the cart's acceleration is approximately 0.611 m/s², and the direction is to the left.
Explanation:
When calculating the acceleration of the cart, we need to consider the net force acting on it and its mass. The net force is found by subtracting the smaller force from the larger force, taking into account their directions. With forces of 140 N to the right and 195 N to the left, the net force is the difference, which is 195 N - 140 N = 55 N, directed to the left since the larger force is in that direction. Using Newton's second law, acceleration (a) is the net force (Fnet) divided by the mass (m).
To find the magnitude of the acceleration, calculate a = Fnet / m. So, a = 55 N / 90 kg which equals approximately 0.611 m/s2. Since the larger force was to the left, the direction of the acceleration is also to the left.
What quantities determine the resistance of a piece of material? Choose all that apply.
The length of the piece of material
The cross-sectional area of the piece of material
The type of material
The voltage across the material
The current flowing through the piece of material
Answer:
Option (a), (b) and (c)
Explanation:
The resistance of a conductor depends on the length of the conductor, area of crossection of the conductor and the nature of the conductor.
The formula for the resistance is given by
R = ρ x l / A
Where, ρ is the resistivity of the conductor, l be the length of the conductor and A be the area of crossection of the conductor.
So, It depends on the length, area and the type of material.
Resistance of a material is determined by its length, cross-sectional area, and the type of material; voltage and current do not determine resistance but are influenced by it.
Explanation:The Quantities Determining the Resistance of a Material
The resistance of a piece of material is determined by several key factors, specifically:
The length of the piece of material: Resistance is directly proportional to the length. The longer the material, the higher the resistance as there will be more collisions between the charges and atoms within the material.The cross-sectional area of the piece of material: Resistance is inversely proportional to the cross-sectional area. Larger areas allow more current to flow, reducing resistance.The type of material: Different materials have different intrinsic resistivity properties, which affect their resistance.It is important to note that the voltage across the material and the current flowing through the material are not factors that determine resistance. These two quantities are actually influenced by the resistance according to Ohm's law, which states that Voltage (V) equals Current (I) times Resistance (R), or V = IR.
A proton travels at a speed 0.25 x 10^7 m/s perpendicular to a magnetic field. The field causes the proton to travel in a circular path of radius 0.975 m. What is the field strength, in tesla?
Answer:
The magnetic field strength of the proton is 0.026 Tesla.
Explanation:
It is given that,
Speed of the proton, [tex]v=0.25\times 10^7\ m/s[/tex]
The radius of circular path, r = 0.975 m
It is moving perpendicular to a magnetic field such that the magnetic force is balancing the centripetal force.
[tex]qvB\ sin90=\dfrac{mv^2}{r}[/tex]
[tex]B=\dfrac{mv}{qr}[/tex]
q = charge on proton
[tex]B=\dfrac{1.67\times 10^{-27}\ kg\times 0.25\times 10^7\ m/s}{1.6\times 10^{-19}\ C\times 0.975\ m}[/tex]
B = 0.026 Tesla
So, the magnetic field strength of the proton is 0.026 Tesla.
A 100.0 g ice cube at -10 degrees Celsius is placed in an aluminum cup whose initial temperature is 70 degrees Celsius. The system come to an equilibrium at 20 degrees Celsius. What is the mass of the cup?
Answer: 135 grams
Explanation:
[tex]Q_{absorbed}=Q_{released}[/tex]
As we know that,
[tex]Q=m\times c\times \Delta T=m\times c\times (T_{final}-T_{initial})[/tex]
[tex]m_1\times c\times (T_{final}-T_1)=-[m_2\times c\times (T_{final}-T_2)][/tex]
where,
[tex]m_1[/tex] = mass of ice = 100 g
[tex]m_2[/tex] = mass of aluminium cup =? g
[tex]T_{final}[/tex] = final temperature =[tex]20^0C[/tex]
[tex]T_1[/tex] = temperature of ice = [tex]-10^oC[/tex]
[tex]T_2[/tex] = temperature of aluminium cup= [tex]70^oC[/tex]
[tex]c_1[/tex] = specific heat of ice= [tex]2.03J/g^0C[/tex]
[tex]c_2[/tex] = specific heat of aluminium cup = [tex] 0.902 J/g^0C[/tex]
Now put all the given values in equation (1), we get
[tex][100\times 2.03\times (20-(-10))]=-[m_2\times 0.902\times (20-70)][/tex]
[tex]m_2=135g[/tex]
Therefore, the mass of the aluminium cup was 135 g.
By calculating the heat transfer between a 100 g ice cube and an aluminum cup, the mass of the cup is found to be approximately 978.3 g.
To solve this, we will use principles of thermal equilibrium and specific heat capacities. Let's go through the steps:
Step 1: Calculate the heat required to warm the ice to 0 degrees Celsius.
The specific heat capacity of ice is 2.1 J/g°C. The formula for heat is:
Q = m * c * ΔT
m = 100.0 g (mass of ice)
c = 2.1 J/g°C (specific heat capacity of ice)
ΔT = (0°C - (-10°C)) = 10°C
Q₁ = 100 g * 2.1 J/g°C * 10°C = 2100 J
Step 2: Calculate the heat required to melt the ice at 0 degrees Celsius.
The enthalpy of fusion of ice ,as we know ,is 334 J/g.
Q₂ = m * L
m = 100.0 g
L = 334 J/g
Q₂ = 100 g * 334 J/g = 33400 J
Step 3: Calculate the heat required to warm the melted ice from 0°C to 20°C.
The specific heat capacity of water is 4.18 J/g°C.
Q₃ = m * c * ΔT
m = 100.0 g
c = 4.18 J/g°C
ΔT = (20°C - 0°C) = 20°C
Q₃ = 100 g * 4.18 J/g°C * 20°C = 8360 J
Step 4: Calculate the total heat gained by the ice.
[tex]Q_{total[/tex] = Q₁ + Q₂ + Q₃ = 2100 J + 33400 J + 8360 J = 43860 J
Step 5: Calculate the heat lost by the aluminum cup.
The specific heat capacity of aluminum is 0.897 J/g°C. Since we need the heat lost, we use:
[tex]Q_{lost[/tex] = m * c * ΔT
[tex]Q_{lost[/tex] = 43860 J
c = 0.897 J/g°C
ΔT = (70°C - 20°C) = 50°C
Rearranging for m:
m = [tex]Q_{lost[/tex] / (c * ΔT)
m = 43860 J / (0.897 J/g°C * 50°C) = 978.3 g
Therefore, the mass of the aluminum cup is approximately 978.3 g.
A person hums into the top of a well and finds that standing waves are established at frequencies of 140, 196, and 252 Hz. The frequency of 140 Hz is not necessarily the fundamental frequency. The speed of sound is 343 m/s. How deep is the well?
Answer:
Depth of well 3.06m
Explanation:
We know that for a pipe closed at one end the frequencies are in ratios if 1:2:3:5:7.... to the fundamental frequency
In our case the given frequencies are in the ratio of
a)[tex]\frac{140}{196}=\frac{5}{7}[/tex]
b) [tex]\frac{196}{252}=\frac{7}{9}[/tex]
Thus the fundamental frequency can be calculated as [tex]140Hz=5n[/tex]
[tex]\therefore n=\frac{140}{5}=28Hz[/tex]
Now we know that
[tex]\lambda_{1}=4l\\\\\frac{v}{f}=4l\\\\l=\frac{v}{4f}[/tex]
Applying values we get
[tex]L=3.06m[/tex]
By identifying 56 Hz as the fundamental frequency and using the formula for the resonance of open-ended tubes, the depth of the well is calculated to be approximately 3.06 meters using the speed of sound as 343 m/s.
Explanation:The student has observed standing waves at frequencies of 140 Hz, 196 Hz, and 252 Hz in a well. These frequencies represent the natural resonant frequencies or harmonics of the well. To find the depth of the well, we need to consider these frequencies as harmonics of a sound wave corresponding to the lengths of the air column in the well where each harmonic creates a standing wave.
Given the multiple frequencies, there is a constant difference of 56 Hz (196 Hz - 140 Hz, 252 Hz - 196 Hz) between consecutive frequencies. This indicates that 56 Hz is the fundamental frequency of the harmonics. We can represent these frequencies as [tex]F1 = 56 Hz \(n=1\), F2 = 112 Hz \(n=2\)[/tex]ere the observed frequencies correspond to F3, F4, and F5.
To determine the length of the well (L), we use the formula for the resonance of open-ended tubes, [tex]\(L = \frac{v}{2f}\)[/tex]d of sound (343 m/s) and 'f' is the frequency (56 Hz in this case). Therefore, [tex]L = \frac{343 m/s}{2 \times 56 Hz} = 3.0625 m[/tex]ly 3.06 meters.
A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x 5 5.00 cm and released from rest at t 5 0. (a) What is the force constant of the spring? (b) What are the angular frequency v, the frequency, and the period of the motion? (c) What is the total energy of the system?
Answer:
a) 250 N/m
b) 22.4 rad/s , 3.6 Hz , 0.28 sec
c) 0.3125 J
Explanation:
a)
F = force applied on the spring = 7.50 N
x = stretch of the spring from relaxed length when force "F" is applied = 3 cm = 0.03 m
k = spring constant of the spring
Since the force applied causes the spring to stretch
F = k x
7.50 = k (0.03)
k = 250 N/m
b)
m = mass of the particle attached to the spring = 0.500 kg
Angular frequency of motion is given as
[tex]w = \sqrt{\frac{k}{m}}[/tex]
[tex]w = \sqrt{\frac{250}{0.5}}[/tex]
[tex]w [/tex] = 22.4 rad/s
[tex]f[/tex] = frequency
Angular frequency is also given as
[tex]w [/tex] = 2 π [tex]f[/tex]
22.4 = 2 (3.14) f
[tex]f[/tex] = 3.6 Hz
[tex]T[/tex] = Time period
Time period is given as
[tex]T = \frac{1}{f}[/tex]
[tex]T = \frac{1}{3.6}[/tex]
[tex]T[/tex] = 0.28 sec
c)
A = amplitude of motion = 5 cm = 0.05 m
Total energy of the spring-block system is given as
U = (0.5) k A²
U = (0.5) (250) (0.05)²
U = 0.3125 J
(a) The force constant of the spring is 250 N/m.
(b) The angular frequency of the mass oscillation is 22.36 rad/s, frequency is 3.56 Hz and the period is 0.28 s.
(c) the total energy of the system is 0.31 J.
Force constant of the springThe force constant of the spring can be determined by applying Hooke's law as follows;
F = kx
k = F/x
k = (7.5)/0.03)
k = 250 N/m
Angular frequencyThe angular frequency of the mass oscillation is calculated as follows;
[tex]\omega = \sqrt{\frac{k}{m} } \\\\\omega = \sqrt{\frac{250}{0.5} }\\\\\omega = 22.36 \ rad/s[/tex]
Angular frequencyThe angular frequency is calculated as follows;
ω = 2πf
f = ω/2π
f = (22.36)/2π
f = 3.56 Hz
Period of the oscillationThe period of the oscillation is calculated as follows;
T = 1/f
T = 1/3.56
T = 0.28 s
Total energy of the systemThe total energy of the system is calculated as follows;
U = ¹/₂kA²
U = ¹/₂ x 250 x (0.05)²
U = 0.31 J
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A wheel starts from rest and rotates with constant angular acceleration and reaches an anaular speed of 12 rad/s in 3 s. Find (a) the magnitude of the angular acceleration of the wheel and (b) the angle (in radian) through which it rotates in this time.
Answer:
(a) 4 rad/s^2
(b) 18 rad
Explanation:
w0 = 0, w = 12 rad/s, t = 3 s
(a) Let α be the angular acceleration.
w = w0 + α t
12 = 0 + 3 α
α = 4 rad/s^2
(b) Let θ be the angle rotated
θ = w0 t + 1/2 α t^2
θ = 0 + 0.5 x 4 x 9
θ = 18 rad
A container of gas is at a pressure of 3.7 × 105 Pa How much work is done by the gas if its volume expands by 1.6 m3?
Answer:
Work is done by the gas = 5.92 x 10⁵ J = 592 kJ
Explanation:
Work done at fixed pressure, W = PΔV
Pressure, P = 3.7 x 10⁵ Pa
Change in volume, ΔV = 1.6 m³
Substituting the values of pressure and change in volume we will get
Work done at fixed pressure, W = PΔV = 3.7 x 10⁵ x 1.6 = 5.92 x 10⁵ J
Work is done by the gas = 5.92 x 10⁵ J = 592 kJ
A snowboarder is at the top of a 90 foot tall slope making an angle of 40 degrees with the horizontal direction. If the snowboarder weighs 170 pounds and the coefficient of friction between the snow and snowboarder is 0.2, what is the snowboarders acceleration down the hill?
Answer:[tex]4.802 m/s^2[/tex]
Explanation:
height of slope(h) =90 foot
[tex]\theta =40[/tex]
weight of snowboarder=170 pounds\approx 77.1107 kg
[tex]\mu =0.2[/tex]
as the snowboarder is sliding down the slope therefore
Now net acceleration of snowboarder is
[tex]a_{net}=gsin\theta -\mu \cdot gcos\theta[/tex]
[tex]a_{net }=9.81\times sin\left ( 40\right )-0.2\times 9.81\times cos\left ( 40\right )[/tex]
[tex]a_{net }=4.802 m/s^2[/tex]
A cylinder which is in a horizontal position contains an unknown noble gas at 4.63 × 104 Pa and is sealed with a massless piston. The piston is slowly, isobarically moved inward 0.163 m, while 1.95 × 104 J of heat is removed from the gas. If the piston has a radius of 0.272 m, calculate the change in internal energy of the system.
Answer:
The change in internal energy of the system is -17746.78 J
Explanation:
Given that,
Pressure [tex]P=4.63\times10^{4}\ Pa[/tex]
Remove heat [tex]\Delta U= -1.95\times10^{4}\ J[/tex]
Radius = 0.272 m
Distance d = 0.163 m
We need to calculate the internal energy
Using thermodynamics first equation
[tex]dU=Q-W[/tex]...(I)
Where, dU = internal energy
Q = heat
W = work done
Put the value of W in equation (I)
[tex]dU=Q-PdV[/tex]
Where, W = PdV
Put the value in the equation
[tex]dU=-1.95\times10^{4}-(4.63\times10^{4}\times3.14\times(0.272)^2\times(-0.163))[/tex]
[tex]dU=-17746.78\ J[/tex]
Hence, The change in internal energy of the system is -17746.78 J
If R is the total resistance of three resistors, connected in parallel, with resistances R1, R2, R3, then 1 R = 1 R1 + 1 R2 + 1 R3 . If the resistances are measured in ohms as R1 = 100 Ω, R2 = 25 Ω, and R3 = 10 Ω, with a possible error of 0.5% in each case, estimate the maximum error in the calculated value of R. (Round your answer to three decimal places.) Ω
To calculate the total resistance of three resistors connected in parallel, use the formula 1/R = 1/R1 + 1/R2 + 1/R3. The maximum error in the calculated value of R can be estimated by multiplying the sum of the errors in each resistance by the calculated value of R.
Explanation:To find the total resistance of three resistors connected in parallel, we use the formula 1/R = 1/R1 + 1/R2 + 1/R3. Given the resistances R1 = 100 Ω, R2 = 25 Ω, and R3 = 10 Ω, we can substitute these values into the formula to calculate the total resistance R. Therefore, 1/R = 1/100 + 1/25 + 1/10 = 0.01 + 0.04 + 0.1 = 0.15. Now, to estimate the maximum error in the calculated value of R, we consider the errors in each resistance. Since each resistance has a possible error of 0.5%, we can calculate the maximum error in R by multiplying the sum of the errors in each resistance by the calculated value of R. Therefore, maximum error in R = 0.005 * 0.15 = 0.00075 Ω.
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The maximum error in the total resistance R of three parallel resistors with a potential error of 0.5% in each resistor is approximately 0.667 ohms.
Explanation:The question asks to calculate the maximum error in the calculated value of total resistance R when three resistors R1, R2, and R3 are connected in parallel, where R1 = 100 Ω, R2 = 25 Ω, and R3 = 10 Ω, each with a possible error of 0.5%. The resistors in parallel have a total resistance denoted by:
1/R = 1/R1 + 1/R2 + 1/R3
To find the maximum error in the calculated value of R, we will first calculate R and then use derivative rules to estimate the maximum error considering the errors in R1, R2, and R3.
After calculating 1/R using the given resistances:
1/R = 1/100 + 1/25 + 1/10
1/R = 0.01 + 0.04 + 0.1 = 0.15
Therefore, R = 1 / 0.15 = 6.667 Ω
We calculate the maximum possible errors in resistances as:
Error in R1 (eR1) = 0.005 * 100 Ω = 0.5 ΩError in R2 (eR2) = 0.005 * 25 Ω = 0.125 ΩError in R3 (eR3) = 0.005 * 10 Ω = 0.05 ΩUsing the formula for the propagation of errors for functions of several independent variables, we estimate the maximum error in R (eR) as:
eR ≈ | -R² * eR1/R1² | + | -R² * eR2/R2² | + | -R² * eR3/R3² |
Plugging in the values:
eR ≈ | -6.667² * 0.5/100² | + | -6.667² * 0.125/25² | + | -6.667² * 0.05/10² |
eR ≈ | -0.04446 | + | -0.17784 | + | -0.4446 | = 0.667 Ω (Approximated to three decimal places)
The estimated maximum error in the calculated value of R is therefore approximately 0.667 Ω.
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A golf ball was thrown with a speed of 25 m/sec at an angle of 65° above the horizontal. What is the horizontal distance traveled by the ball before it hits the ground?
Answer:
The horizontal distance traveled by the ball before it hits the ground is 48.85 meters.
Explanation:
It is given that,
Speed of golf ball, v = 25 m/s
Angle above horizontal or angle of projection, θ = 65°
We need to find the distance travelled by the ball before it hots the ground or in other words we need to find the range. It is given by R.
[tex]R=\dfrac{v^2\ sin2\theta}{g}[/tex]
[tex]R=\dfrac{(25\ m/s)^2\ sin2(65)}{9.8\ m/s^2}[/tex]
R = 48.85 m
So, the distance travelled by the ball before it hots the ground is 48.85 meters. Hence, this is the required solution.
What is the magnitude of the electric force on an electron in a uniform electric field of strength 1500 N/C that points due east?
Answer:
The magnitude of the electric force on an electron in a uniform electric is [tex]2.4\times10^{-16}\ N[/tex] to the west.
Explanation:
Given that,
Electric field strength = 1500 N/C
We need to calculate the electric force
Using formula of electric field
[tex]F = Eq[/tex]
E = electric field strength
q = charge of electron
Electron has negative charge.
Put the value into the formula
[tex]F=1500\times(-1.6\times10^{-19})[/tex]
[tex]F=-2.4\times10^{-16}\ N[/tex]
Negative sign shows the opposite direction of the field
Hence, The magnitude of the electric force on an electron in a uniform electric is [tex]2.4\times10^{-16}\ N[/tex] to the west.
The magnitude of the electric force on an electron in a uniform electric field of strength 1500 N/C that points due east is 2.4x10⁻¹⁶ C.
What is the magnitude of the electric force?We know that electric force is given by the formula,
[tex]F = E \times q[/tex]
It is given that the electric field, E = 1500 N/C,
We also know that an electron is negatively charged and has a charge of 1.60217662 × 10⁻¹⁹ C.
[tex]F = E \times q\\\\F = 1500 \times 1.6 \times 10^{-19}\\\\F = 2.4 \times 10^{-16}\rm\ N[/tex]
Hence, the magnitude of the electric force on an electron in a uniform electric field of strength 1500 N/C that points due east is 2.4x10⁻¹⁶ C.
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Two small plastic spheres each have a mass of 1.1 g and a charge of -50.0 nC . They are placed 2.1 cm apart (center to center). A. What is the magnitude of the electric force on each sphere? B. By what factor is the electric force on a sphere larger than its weight?
Answer:
Part a)
F = 0.051 N
Part b)
Both spheres will follow Newton's III law of action reaction force so both sphere will have same force of equal magnitude.
Explanation:
Part a)
Electrostatic force between two charged spherical balls is given as
[tex]F = \frac{kq_1q_2}{r^2}[/tex]
here we will have
[tex]q_1 = q_2 = 50 nC[/tex]
here the distance between the center of two balls is given as
[tex]r = 2.1 cm = 0.021 m[/tex]
now we will have
[tex]F = \frac{(9\times 10^9)(50 \times 10^{-9})(50 \times 10^{-9})}{0.021^2}[/tex]
[tex]F = 0.051 N[/tex]
Part b)
Both spheres will follow Newton's III law of action reaction force so both sphere will have same force of equal magnitude.
A moon is in orbit around a planet. The moon's orbit has a semimajor axis of 4.3 times 10 Superscript 8 Baseline m and has an orbital period of 1.516 days. Use these data to estimate the mass of the planet.
Answer:
The mass of the planet is [tex]2.7\times10^{27}\ kg[/tex].
Explanation:
Given that,
Semi major axis [tex]a= 4.3\times10^{8}[/tex]
Orbital period T=1.516 days
Using Kepler's third law
[tex]T^2=\dfrac{4\pi^2}{GM}a^3[/tex]
[tex]M=\dfrac{4\pi^2}{GT^2}a^3[/tex]
Where, T = days
G = gravitational constant
a = semi major axis
Put the value into the formula
[tex]M=\dfrac{4\times(3.14)^2}{6.67\times10^{-11}(1.516\times24\times60\times60)^2}(4.3\times10^{8})^3[/tex]
[tex]M=2.7\times10^{27}\ kg[/tex]
Hence, The mass of the planet is [tex]2.7\times10^{27}\ kg[/tex].