Answer:
(a) 3.13 m/s
(b) 9.9 m/s
(c) 7.73 m/s
Explanation:
u = 0 m/s, g = 9.8 m/s^2
Let v be the velocity of ball as it hit the ground.
(a) h = 0.5 m
Use third equation of motion.
v^2 = u^2 + 2 g h
v^2 = 0 + 2 x 9.8 x 0.5
v^2 = 9.8
v = 3.13 m/s
(b) h = 5 m
Use third equation of motion.
v^2 = u^2 + 2 g h
v^2 = 0 + 2 x 9.8 x 5
v^2 = 98
v = 9.9 m/s
(c) h = 10 feet = 3.048 m
Use third equation of motion.
v^2 = u^2 + 2 g h
v^2 = 0 + 2 x 9.8 x 3.048
v^2 = 59.74
v = 7.73 m/s
Work is required to compress 5.00 mol of air at 20.00C and 1.00 atm to one-tenth of the original volume by an adiabatic process. How much work is required to produce this same compression?
Answer:46.03 KJ
Explanation:
no of moles(n)=5
temperature of air(T)=[tex]20^{\circ}[/tex]
pressure(p)=1 atm
final volume is [tex]\frac{V}{10}[/tex]
We know work done in adaibatic process is given by
W=[tex]\frac{P_iV_i-P_fV_f}{\gamma -1}[/tex]
[tex]\gamma[/tex] for air is 1.4
we know [tex]P_iV_i^{\gamma }= P_fV_f^{\gamma }[/tex]
[tex]1\left ( V\right )^{\gamma }[/tex]=[tex]P_f\left (\frac{v}{10}\right )^{\gamma }[/tex]
[tex]10^{\gamma }=P_f[/tex]
[tex]P_f=25.118 atm[/tex]
W=[tex]\frac{1\times 0.1218-25.118\times 0.01218}{1.4 -1}[/tex]
W=-46.03 KJ
it means work is done on the system
You are in a fire truck heading directly toward a tunnel in a mountainside at 17m/s. you hear the truck's 90Hz siren as well as its reflection from the mountainside. What beat frequency do you hear?
Hey there!:
Take the speed of sound to be 343m/s.
Direct frequency perceived by observer:
(343 + 17) / 343) * 90Hz = 94.460Hz
Change in frequency = ( 4.460 - 90 ) = 4.460Hz.
90 - (4.460 x 2) = 81.08 Hz. indirect frequency heard by observer.
Therefore :
Beat frequency = (94.460 - 81.08) = 13.38Hz.
Hope this helps!
A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15°, and rolls to the bottom. The upper end of the ramp is 1.2 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp
The Linear speed of the sphere is mathematically given as
v = 4.1 m/s
What is the linear speed of the sphere when it reaches the bottom of the ramp?Question Parameter(s):
A solid sphere of mass 4.0 kg and radius of 0.12 m starts from rest at the top of a ramp inclined 15°
Generally, the equation for the conservation of energy is mathematically given as
[tex]mgh = \frac{1}{2}mv^2 + \frac{1}{2}Iw^2[/tex]
Therefore
[tex]mgh = \frac{1}{2}mv^2 + \frac{1}{2}(\frac{2}{5}mR^2)(\frac{v^2}{R^2})\\\\mgh = \frac{7}{10}mv^2[/tex]
In conclusion, the Speed is
[tex]v^2 = \sqrt{\frac{10}{7}(9.8)(1.2)}[/tex]
v = 4.1 m/s
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The linear speed of the sphere when it reaches the bottom of the ramp is approximately[tex]\( 4.85 \, \text{m/s} \).[/tex]
At the top of the ramp, the potential energy U of the sphere is given by:
[tex]\[ U = mgh \][/tex]
where m is the mass of the sphere, g is the acceleration due to gravity (approximately[tex]\( 9.8 \, \text{m/s}^2[/tex], and h is the height of the ramp.
At the bottom of the ramp, the kinetic energy K of the sphere is given by:
[tex]\[ K = \frac{1}{2}mv^2 \][/tex]
where v is the linear speed of the sphere.
Since energy is conserved, we have:
U = K
[tex]\[ mgh = \frac{1}{2}mv^2 \][/tex]
We can solve for v by canceling the mass m from both sides and multiplying through by 2:
[tex]\[ 2gh = v^2 \][/tex]
Taking the square root of both sides gives us the linear speed v :
[tex]\[ v = \sqrt{2gh} \][/tex]
Given that the height h is 1.2 m and the acceleration due to gravity g is [tex]\( 9.8 \, \text{m/s}^2 \)[/tex], we can plug in these values:
[tex]\[ v = \sqrt{2 \times 9.8 \, \text{m/s}^2 \times 1.2 \, \text{m}} \][/tex]
[tex]\[ v = \sqrt{23.52 \, \text{m}^2/\text{s}^2} \][/tex]
[tex]\[ v \ =4.85 \, \text{m/s} \][/tex]
The addition of heat Q causes a metal object to increase in temperature from 4°C to 6°C . What is the amount of heat necessary to increase the object's temperature from 6°C to 12°C? 4Q 2Q Q 3Q
Answer:
The answer is 3Q
Explanation:
The metal temperature increases in a linear way, we could get a difference between final and initial temperature
[tex]DT=FinalTemperature-InitialTemperature[/tex]
We get a temperature difference of 2 degrees per each heat addition. If we add the same heat 3 times more, it will increase to 12 degrees
Answer:
The quantity of heat required to increase the temperature of the object from 6°C to 12°C is 3Q
Explanation:
Heat capacity is the quantity of heat required to increase the temperature of an object.
Q = mcΔθ
where;
Q is the quantity of heat
m is the mass of the object
c is specific heat capacity of the object
Δθ is change in temperature = T₂ - T₁
For the first sentence of this question;
Q = mc(6-4)
Q = mc(2)
Q = 2mc
For the second sentence of this question;
Let Q₂ be the quantity of heat required to increase the temperature of the object from 6°C to 12°C
Q₂ = mcΔθ
Q₂ = mc(12-6)
Q₂ = mc(6)
Q₂ = 6mc
Q₂ = 3(2mc)
Recall, Q = 2mc
Thus, Q₂ = 3Q
A car of mass 2800 kg collides with a truck of mass 4000 kg, and just after the collision the car and truck slide along, stuck together, with no rotation. The car's velocity just before the collision was <36, 0, 0> m/s, and the truck's velocity just before the collision was <-15, 0, 29> m/s. (a) Your first task is to determine the velocity of the stuck-together car and truck just after the collision. (d) What is the increase in internal energy of the car and truck (thermal energy and deformation)?
(a) The velocity of the car-truck system after collision is 18.08 m/s.
(b) The increase in internal energy of the car and truck is 2,835,031.2 J.
Velocity of the truck - car system after collision
The velocity of the system after collision is determined by applying the principle of conservation of linear momentum as shown below;
Final velocity in x - directionm₁u₁ + m₂u₂ = v(m₁ + m₂)
2800(36) + 4000(-15) = vx(2800 + 4000)
40,800 = 6800vx
vx = 6 m/s
Final velocity in z - directionm₁u₁ + m₂u₂ = v(m₁ + m₂)
2800(0) + 4000(29) = vz(2800 + 4000)
116,000 = 6800vz
vz = 17.06 m/s
Resultant velocity of the car-truck system after the collision [tex]v= \sqrt{v_x^2 + v_z^2} \\\\v = \sqrt{6^2 + 17.06^2} \\\\v = 18.08 \ m/s[/tex]Initial kinetic energy of the car and truckK.E(car) = ¹/₂mv²
K.E(car) = ¹/₂ x (2800) x (36)²
K.E(car) = 1,814,400 J
v(truck) = √(15² + 29²) = 32.65
K.E(truck) = ¹/₂ x (4000) x (32.65)²
K.E(truck) = 2,132,045 J
K.E(total) = 1,814,400 J + 2,132,045 J = 3,946,445 J
Final kinetic energy of the systemK.E = ¹/₂(m₁ + m₂)v²
K.E = ¹/₂ x (2800 + 4000) x (18.08)²
K.E = 1,111,413.8 J
Increase in internal energyU = ΔK.E
U = 3,946,445 J - 1,111,413.8 J
U = 2,835,031.2 J
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Final answer:
To determine the velocity of the stuck-together car and truck after the collision, apply the principle of conservation of momentum. Consider the change in kinetic energy and the production of thermal energy and deformation.
Explanation:
To determine the velocity of the stuck-together car and truck just after the collision, we can apply the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision. We can find the final velocity by summing the momenta of the car and truck and dividing by their combined mass.
In this case, the car's momentum is the product of its mass and velocity, and the truck's momentum is the product of its mass and velocity. Adding these momenta together and dividing by the combined mass gives us the final velocity of the stuck-together car and truck just after the collision.
For the increase in internal energy of the car and truck, we need to consider the change in kinetic energy and the production of thermal energy and deformation. The change in kinetic energy can be calculated by finding the difference between the initial and final kinetic energies of the car and truck. The thermal energy and deformation depend on factors such as the materials involved and the severity of the collision.
What is the magnetic flux density (B-field) at a distance of 0.36 m from a long, straight wire carrying a current of 3.8 A in air? Give your answer in units of tesla.
Answer:
The magnetic flux density is [tex]2.11\times10^{-6}\ T[/tex]
Explanation:
Given that,
Distance = 0.36 m
Current = 3.8 A
We need to calculate the magnetic flux density
Using formula of magnetic field
[tex]B =\dfrac{\mu_{0}I}{2r}[/tex]
Where,
r = radius
I = current
Put the value into the formula
[tex]B =\dfrac{4\pi\times10^{-7}\times3.8}{2\times\pi\times0.36}[/tex]
[tex]B=2.11\times10^{-6}\ T[/tex]
Hence, The magnetic flux density is [tex]2.11\times10^{-6}\ T[/tex]
An electric field of magnitude 2.35 V/m is oriented at an angle of 25.0° with respect to the positive z-direction. Determine the magnitude of the electric flux througha rectangular area of 1.65 m2 in the xy-plane. N m2/C
Answer:
The magnitude of the electric flux is [tex]3.53\ N-m^2/C[/tex]
Explanation:
Given that,
Electric field = 2.35 V/m
Angle = 25.0°
Area [tex]A= 1.65 m^2[/tex]
We need to calculate the flux
Using formula of the magnetic flux
[tex]\phi=E\cdot A[/tex]
[tex]\phi = EA\cos\theta[/tex]
Where,
A = area
E = electric field
Put the value into the formula
[tex]\phi=2.35\times1.65\times\cos 25^{\circ}[/tex]
[tex]\phi=2.35\times1.65\times0.91[/tex]
[tex]\phi=3.53\ N-m^2/C[/tex]
Hence, The magnitude of the electric flux is [tex]3.53\ N-m^2/C[/tex]
Lonnie pitches a baseball of mass 0.20 kg. The ball arrives at home plate with a speed of 40 m/s and is batted straight back to Lonnie with a return speed of 60 m/s. If the bat is in contact with the ball for 0.050 s what is the impulse experienced by the ball? A. 360 N.s B. 20 N.s C. 400 N.s D. 9.0 N.s
Answer:
B) 20N.s is the correct answer
Explanation:
The formula for the impulse is given as:
Impulse = change in momentum
Impulse = mass × change in speed
Impulse = m × ΔV
Given:
initial speed = 40m/s
Final speed = -60 m/s (Since the the ball will now move in the opposite direction after hitting the bat, the speed is negative)
mass = 0.20 kg
Thus, we have
Impulse = 0.20 × (40m/s - (-60)m/s)
Impulse = 0.20 × 100 = 20 kg-m/s or 20 N.s
The impulse experienced by the ball is,
[tex]\rm Impulse = 20\; Nsec[/tex]
Given :
Mass = 0.20 Kg
Initial Speed = 40 m/sec
Final Speed = -60 m/sec (minus sign shows that ball move in opposite direction)
Solution :
We know that the formula of Impulse is,
[tex]\rm Impulse = m\times \Delta V[/tex]
where, m is the mass and [tex]\rm \Delta V[/tex] is change in velocity.
[tex]\rm Impulse = 0.20\times(40-(-60))[/tex]
[tex]\rm Impulse = 20\; Nsec[/tex]
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If T is the absolute temperature, the intensity of radiation from an ideal radiator will be proportional to (a) T (b) T (c) T (d) T (e) none of the above
Answer:
T^4
Explanation:
According to the Stefan's law, the energy radiated per unit time and per unit area is directly proportional to the four power of teh absolute temperature of the black body.
E ∝ T^4
The intensity of radiation from an ideal radiator is not directly proportional to the absolute temperature T, but rather to T4, according to the Stefan-Boltzmann law of radiation.
Explanation:The intensity of radiation from an ideal radiator, or blackbody, is not directly proportional to the absolute temperature T; instead, it follows the Stefan-Boltzmann law of radiation. This law states that the intensity of radiation, referred to as 'P' or power, is directly proportional to the fourth power of the absolute temperature (P = σAT4). Here, σ (sigma) represents Stefan-Boltzmann constant, A denotes surface area, and T signifies absolute temperature.
This means the answer to your question is none of the above, as the intensity of the radiation isn't directly proportional to T, but rather to T4.
As an example, considering two temperatures T₁ = 293 K and T₂ = 313 K, the rate of heat transfer with T₂ is about 30 percent higher than T₁. This showcases the considerable impact of temperature on radiation intensity.
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A rock is thrown from the top of a 20-m building at an angle of 53° above the horizontal. If the horizontal range of the throw is equal to the height of the building, with what speed was the rock thrown? What is the velocity of the rock just before it strikes the ground?
By using equations from physics pertaining to projectile motion and manipulation of initial velocity, final velocity components, and combined final velocity, we can calculate the initial speed at which the rock was thrown and its velocity just before striking the ground.
Explanation:The subject of this question is projectile motion, a branch of physics. Given that the horizontal range of the throw is equal to the height of the building, we can apply the equation for range in projectile motion: R = (v² sin 2α) / g, where R is the range (20m), v is velocity, α is the angle (53 degrees), and g is acceleration due to gravity (approx. 9.8 m/s²).
Firstly, solve the equation for v which gives v = sqrt(R * g / sin 2α). This gives the starting speed of the rock.
To find the final velocity just before hitting the ground, we need to find vertical and horizontal components of velocity. Vertical component can be obtained by using: v_f = sqrt(v_i² + 2*g*h), h is the height(20m). Horizontal component remains constant which is v_i*cosα. The final velocity is then, sqrt(v_h² + v_f²).
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In 2 1/2 hours an airplane travels 1150 km against the wind. It takes 50 min to travel 450 km with the wind. Find the speed of the wind and the speed of the airplane in still air. g
Answer:
Velocity of airplane is 500 km/h
Velocity of wind is 40 km/h
Explanation:
[tex]V_a[/tex]= Velocity of airplane in still air
[tex]V_w[/tex]= Velocity of wind
Time taken by plane to travel 1150 km against the wind is 2.5 hours
[tex]V_a-V_w=\frac {1150}{2.5}\\\Rightarrow V_a-V_w=460\quad (1)[/tex]
Time taken by plane to travel 450 km against the wind is 50 minutes = 50/60 hours
[tex]V_a+V_w=\frac {450}{50}\times 60\\\Rightarrow V_a-V_w=540\quad (2)[/tex]
Subtracting the two equations we get
[tex]V_a-V_w-V_a-V_w=460-540\\\Rightarrow -2V_w=-80\\\Rightarrow V_w=40\ km/h[/tex]
Applying the value of velocity of wind to the first equation
[tex]V_a-40=460\\\Rightarrow V_a =500\ km/h[/tex]
∴ Velocity of airplane in still air is 500 km/h and Velocity of wind is 40 km/h
The given mathematical problem involves calculating speeds. The speed of the airplane in still air was found to be 501 km/h and the wind speed was calculated to be 41 km/h, by using the concept of speed equals distance divided by time.
Explanation:The subject is related to measurements of speed, which is essentially a mathematical problem, specifically involving algebraic calculations. In order to solve this problem, we will use the concept that speed equals distance divided by time.
Firstly, convert all time measurements to the same unit. Since the speed of an airplane is typically measured in km/h, it will be convenient to convert the 50 minutes to hours (50/60 = 0.83 hours).
When moving against the wind, the combined speed (airplane speed minus wind speed) is 1150 km / 2.5 h = 460 km/h. When moving with the wind, the combined speed (airplane speed plus wind speed) becomes 450 km / 0.83 h = 542 km/h.
Now you can find the speed of the airplane in still air by averaging the two combined speeds: (460 km/h + 542 km/h) / 2 = 501 km/h. The speed of the wind can be found by subtracting the airplane's speed from the higher combined speed: 542 km/h - 501 km/h = 41 km/h. Therefore, the speed of the airplane in still air is 501 km/h and the wind speed is 41 km/h.
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A 0.7 kg lab cart moving to the right at 0.15 m/s collides with a 0.5 kg lab cart moving to the right at 0.10 m/s. After the collision, the 0.7 kg cart is moving to the right at 0.08 m/s. Calculate the velocity of the 0.5 kg lab cart after the collision.
Answer:
0.198 m/s
Explanation:
m1 = 0.7 kg, u1 = 0.15 m/s,
v1 = 0.08 m/s
m2 = 0.5 kg, u2 = 0.1 m/s
Let the speed of 0.5 kg is v2 after the collision.
By using the conservation of momentum
Momentum before collision = momentum after collision
m1 u1 + m2 u2 = m1 v1 + m2 v2
0.7 x 0.15 + 0.5 x 0.1
= 0.7 × 0.08 + 0.5 × v2
0.099 = 0.5 v2
v2 = 0.198 m/s
Many Amtrak trains can travel at a top speed of 42.0 m/s. Assuming a train maintains that speed for several hours, how many kilometers will the train have traveled after 4.00 hours? Round to the nearest km.
Answer:
605 km
Explanation:
Hello
the same units of measure should be used, then
Step 1
convert 42 m/s ⇒ km/h
1 km =1000 m
1 h = 36000 sec
[tex]42 \frac{m}{s}*\frac{1\ km}{1000\ m}=0.042\ \frac{km}{s}\\ 0.042\ \frac{km}{s}\\[/tex]
[tex]0.042\ \frac{km}{s}*\frac{3600\ s}{1\ h} =151.2 \frac{km}{h}\\ \\Velocity =151.2\ \frac{km}{h}[/tex]
Step 2
find kilometers traveled after 4 hours
[tex]V=\frac{s}{t}\\ \\[/tex]
V,velocity
s, distance traveled
t. time
now, isolating s
[tex]V=\frac{s}{t} \\s=V * t\\[/tex]
and replacing
[tex]s=V * t\\s=151.2\frac{km}{h}*4 hours\\ s=604.8 km\\[/tex]
S=604.8 Km
Have a great day
If the charge of a particle doubles, what happens to the force acting on it?
It doubles
It gets reduced by a factor of two
It stays the same
A charge exerts a negative force on another charge. Does that mean that:
Both charges are positive
Both charges are negative
the charges are of opposite signs
please explain this throughly! thanks
Explanation:
(1) The force that exists between charged particles is electrostatic force. It is given by :
[tex]F=k\dfrac{q_1q_2}{r^2}[/tex]
Where
q₁ and q₂ are charges
r is distance between charges
If the charge of a particle doubles, the electric force doubles. So, the correct option is (a) "It doubles".
(2) A charge exerts a negative force on another charge. Negative force denotes the force is attractive. It means that the charges are of opposite sign. So, the correct option is (c) "the charges are of opposite signs".
A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle θ = 30°. The sphere has mass M = 8 kg and radius R = 0.19 m . The coefficient of static friction between the sphere and the plane is μ = 0.64. What is the magnitude of the frictional force on the sphere?
Answer:
40N
Explanation:
frictional force = mgsin©
frictional force = 8*10*sin30
frictional force = 8*10*0.5= 40N//
A rigid tank contains 1.80 moles of helium, which can be treated as an ideal gas, at a pressure of 27.3 atm. While the tank and gas maintain a constant volume and temperature, a number of moles are removed from the tank, reducing the pressure to 5.20 atm. How many moles are removed?
Answer:
Has been removed 1.458 moles.
Explanation:
n1= 1.8 mol
p1= 27.3 atm
p2= 5.2 atm
n2= ?
n2= n1 * p2/p1
n2= 0.342 moles
Δn= n1-n2
Δn= 1.458 moles
A vertically mounted spring (k = 750 N/m) is compressed by 35.0 cm relative to its unstrained length. A mass (m = 0.36 kg) is placed at rest against the spring. When the spring is released, the mass is launched vertically in the air. How high from release point the mass can reach?
Answer:
Height, h = 13.02 meters
Explanation:
It is given that,
Spring constant of the spring, k = 750 N/m
It is compressed by 35 cm relative to its unstained length, x = 35 cm = 0.35 m
Mass of the object, m = 0.36 kg
When the spring is released, the mass is launched vertically in the air. We need to find the height attained by the mass at this position. On applying the conservation of energy as :
Energy stored in the spring = change on potential energy
[tex]\dfrac{1}{2}kx^2=mgh[/tex]
[tex]h=\dfrac{kx^2}{2mg}[/tex]
[tex]h=\dfrac{750\ N/m\times (0.35\ m)^2}{2\times 0.36\ kg\times 9.8\ m/s^2}[/tex]
h = 13.02 meters
So, the mass will reach a height of 13.02 meters. Hence, this is the required solution.
The maximum height reached by the mass when the spring is released is 13.02 m.
The given parameters;
spring constant, k = 750 N/mextension of the spring, x = 35 cm = 0.35 mmass attached, m = 0.36 kgApply the principle of conservation energy to determine the maximum height reached by the mass when the spring is released.
mgh = ¹/₂kx²
where;
h is the maximum height reached by the massg is acceleration due to gravity[tex]h = \frac{kx^2}{2mg} \\\\h = \frac{(750) \times (0.35)^2}{2(0.36\times 9.8)} \\\\h = 13.02 \ m[/tex]
Thus, the maximum height reached by the mass when the spring is released is 13.02 m.
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A uniform disk of mass 20.0 kg and radius 20.0 cm has an additional rim of mass 20.0 kg as well as four symmetrically placed masses, each of mass 1/4th of the mass of the disk, fastened at positions having position vectors (10.0 i + 10.0 j) cm, (10.0 i - 10.0 j) cm, (-10.0i - 10.0 j cm, (-10.0 i + 10.0 j) cm (with respect to the center of the disk). What is the moment of inertia of the whole unit about an axis perpendicular to the disk and passing through its center?
Answer:
[tex]I = 1.6 kg m^2[/tex]
Explanation:
Moment of inertia of disc is given as
[tex]I = \frac{1}{2}mR^2[/tex]
now we have
m = 20 kg
R = 20.0 cm = 0.20 m
now we have
[tex]I_{disc} = \frac{1}{2}(20 kg)(0.20 m)^2[/tex]
[tex]I_{disc} = 0.4 kg m^2[/tex]
Now the additional mass of 20 kg is placed on its rim so it will behave as a ring so moment of inertia of that part of the disc is
[tex]I = mR^2[/tex]
m = 20 kg
R = 20 cm = 0.20 m
[tex]I_{ring} = 20(0.20^2)[/tex]
[tex]I_{ring} = 0.8 kg m^2[/tex]
Now four point masses each of the mass of one fourth of mass of disc is placed at four positions so moment of inertia of these four masses is given as
[tex]I_{mass} = 4( m'r^2)[/tex]
here we have
[tex]m' = \frac{m}{4}[/tex]
[tex]I_{mass} = 4(\frac{m}{4})(0.10^2 + 0.10^2)[/tex]
[tex]I_{mass} = 20(0.02) = 0.40 kg m^2[/tex]
Now total moment of inertia of the system is given as
[tex]I = I_{disc} + I_{ring} + I_{mass}[/tex]
[tex]I = 0.4 + 0.8 + 0.4 = 1.6 kg m^2[/tex]
The blackbody radation emmitted from a furnace peaks at a wavelength of 1.9 x 10^-6 m (0.0000019 m). what is the temperature inside the furnace?
Answer:
Temperature, T = 1542.10 K
Explanation:
It is given that,
The black body radiation emitted from a furnace peaks at a wavelength of, [tex]\lambda=1.9\times 10^{-6}\ m[/tex]
We need to find the temperature inside the furnace. The relationship between the temperature and the wavelength is given by Wein's law i.e.
[tex]\lambda\propto \dfrac{1}{T}[/tex]
or
[tex]\lambda=\dfrac{b}{T}[/tex]
b = Wein's displacement constant
[tex]\lambda=\dfrac{2.93\times 10^{-3}}{T}[/tex]
[tex]T=\dfrac{2.93\times 10^{-3}}{\lambda}[/tex]
[tex]T=\dfrac{2.93\times 10^{-3}}{1.9\times 10^{-6}\ m}[/tex]
T = 1542.10 K
So, the temperature inside the furnace is 1542.10 K. Hence, this is the required solution.
Using Wien's Displacement Law, the temperature inside a furnace emitting radiation that peaks at a wavelength of 1.9 x 10^-6 m is approximately 1525 Kelvin.
Explanation:The temperature of the furnace can be determined using Wien's Displacement Law, which states that the product of the temperature of a black body and the wavelength at which the radiation it emits is most intense is approximately equal to 2.898 x 10^-3 m.K. In this specific case, the peak wavelength of the energy emitted from the furnace is given as 1.9 x 10^-6 m. Therefore, the temperature inside the furnace can be calculated using the formula: T = Amax / λ, where Amax = 2.898 x 10^-3 m.K and λ = 1.9 x 10^-6 m. Calculating from the given formula, T ≈ 1525 K. Therefore, the temperature inside the furnace is approximately 1525 Kelvin.
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You heat a 541cm^3 sample of a substance from 133°C to 273°C and find that its volume increases by 2.25 cm^3. Calculate the coefficient of volume expansion of this substance.
Answer:
[tex]\gamma = 2.97 \times 10^{-5} per ^0 C[/tex]
Explanation:
As we know by the theory of expansion the change in the volume of the object is directly proportional to change in temperature and initial volume.
So here we can say
[tex]\Delta V = V_0\gamma \Delta T[/tex]
here
[tex]\gamma[/tex] = coefficient of volume expansion
so we have
[tex]\gamma = \frac{\Delta V}{V_0 \Delta T}[/tex]
now plug in all values
[tex]\gamma = \frac{2.25 cm^3}{(541 cm^3)(273 - 133)}[/tex]
[tex]\gamma = 2.97 \times 10^{-5} per ^0 C[/tex]
what is the de broglie wavelength of 10 Mev electron
Answer:
The wave length is [tex]3.885\times10^{-13}\ m[/tex]
Explanation:
Given that,
Energy = 10 Mev
We need to calculate the wavelength
Using formula of debroglie wave length
[tex]\lambda=\dfrac{h}{\sqrt{2mE}}[/tex]
Where, h = Planck constant
E = energy
m = mass
Put the value into the formula
[tex]\lambda =\dfrac{6.634\times10^{-34}}{\sqrt{2\times9.11\times10^{-31}\times10\times10^{6}\times1.6\times10^{-19}}}[/tex]
[tex]\lambda=3.885\times10^{-13}\ m[/tex]
Hence, The wave length is [tex]3.885\times10^{-13}\ m[/tex]
A disk between vertebrae in the spine is subjected to a shearing force of 600 N. Find its shear deformation, taking it to have a shear modulus of 1x10^9 N/m^2. The disk is equivalent to a solid cylinder 0.700 cm high and 4.00 cm in diameter. a)3 μm
b)3 mm
c)3 cm
d)3 km
Answer:
The shear deformation is [tex]\Delta x=3.34\times10^{-6}\ m[/tex].
Explanation:
Given that,
Shearing force F = 600 N
Shear modulus [tex]S = 1\times10^{9}\ N/m^2[/tex]
length = 0.700 cm
diameter = 4.00 cm
We need to find the shear deformation
Using formula of shear modulus
[tex]S=\dfrac{Fl_{0}}{A\Delta x}[/tex]
[tex]\Delta x=\dfrac{Fl_{0}}{(\dfrac{\pi d^2}{4})S}[/tex]
[tex]\Delta x=\dfrac{4Fl_{0}}{\pi d^2 S}[/tex]
Put the value into the formula
[tex]\Delta x=\dfrac{4\times600\times0.700\times10^{-2}}{3.14\times1\times10^{9}\times(4.00\times10^{-2})^2}[/tex]
[tex]\Delta x=3.34\times10^{-6}\ m[/tex]
Hence, The shear deformation is [tex]\Delta x=3.34\times10^{-6}\ m[/tex].
The shear deformation experienced by the disc is calculated using a formula that takes into account the shear modulus, the force applied, and the cross-sectional area of the disk. The correct answer is found to be approximately 0.478 μm.
Explanation:Solving this problem involves understanding the formula for shear deformation, which is the ratio of the applied force to the area of the disc over which it is applied, multiplied by the height of the disc and divided by the shear modulus.
First, we need to calculate the cross-sectional area of the disk. The formula for the area of a circle is πr², where r is the radius of the disc. Given the diameter of 4 cm, the radius is 2 cm or 0.02 m. So, the area = π * (0.02)² = 0.001256 m².
Substituting into the formula for shear deformation, we get τ = F / (G * A) which equals 600 N / (1x10^9 N/m² * 0.001256 m²) = 4.78x10^-7 m or approximately 0.478 μm.
This indicates that none of the initial answers are correct. The closest incorrect answer is 3 μm but the correct answer is 0.478 μm.
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A 9.0 µF capacitor is charged by a 13.0 V battery through a resistance R. The capacitor reaches a potential difference of 4.00 V at a time 3.00 s after charging begins. Find R.
Answer:
9.1 x 10⁵ ohm
Explanation:
C = Capacitance of the capacitor = 9 x 10⁻⁶ F
V₀ = Voltage of the battery = 13 Volts
V = Potential difference across the battery after time "t" = 4 Volts
t = time interval = 3 sec
T = Time constant
R = resistance
Potential difference across the battery after time "t" is given as
[tex]V = V_{o} (1-e^{\frac{-t}{T}})[/tex]
[tex]4 = 13 (1-e^{\frac{-3}{T}})[/tex]
T = 8.2 sec
Time constant is given as
T = RC
8.2 = (9 x 10⁻⁶) R
R = 9.1 x 10⁵ ohm
Final answer:
To determine the resistance R, the RC circuit charging equation is used with the given values. By rearranging the equation and solving, the resistance R is found to be approximately 7.97 kΩ.
Explanation:
To find the resistance R in the given circuit, we use the charging equation for a capacitor in an RC circuit:
V(t) = V_0(1 - e^{-t/RC})
Where V(t) is the voltage across the capacitor at time t, V_0 is the initial voltage provided by the battery, R is the resistance, C is the capacitance, and t is the time.
Plugging in the given values:
V(t) = 4.00 V
V_0 = 13.0 V
C = 9.0 µF
t = 3.00 s
We have:
4.00 = 13.0(1 - e^{-3/(9.0×10^{-6}R)})
Now solve for R:
1 - \frac{4.00}{13.0} = e^{-3/(9.0×10^{-6}R))}
Simplifying:
\frac{9.00}{13.00} = e^{-3/(9.0×10^{-6}R))}
Take the natural logarithm of both sides:
ln(\frac{9.00}{13.00}) = -\frac{3}{9×10^{-6}R}
Multiply by -9×10^{-6}R and divide by 3:
R = -\frac{9×10^{-6}ln(\frac{9.00}{13.00})}{3}
R ≈ 7.97 kΩ
Thus, the resistance R is approximately 7.97 kΩ.
A skateboarder shoots off a ramp with a velocity of 6.6 m/s, directed at an angle of 58 above the horizontal. The end of the ramp is 1.2 m above the ground. Let the x axis be parallel to the ground, the +y direction be vertically upward, and take as the origin the point on the ground directly below the top of the ramp. (a) How high above the ground is the highest point that the skateboarder reaches? (b) When the skateboarder reaches the highest point, how far is this point horizontally from the end of the ramp?
Answer:
a) Maximum height reached above ground = 2.8 m
b) When he reaches maximum height he is 2 m far from end of the ramp.
Explanation:
a) We have equation of motion v²=u²+2as
Considering vertical motion of skateboarder.
When he reaches maximum height,
u = 6.6sin58 = 5.6 m/s
a = -9.81 m/s²
v = 0 m/s
Substituting
0²=5.6² + 2 x -9.81 x s
s = 1.60 m
Height above ground = 1.2 + 1.6 = 2.8 m
b) We have equation of motion v= u+at
Considering vertical motion of skateboarder.
When he reaches maximum height,
u = 6.6sin58 = 5.6 m/s
a = -9.81 m/s²
v = 0 m/s
Substituting
0= 5.6 - 9.81 x t
t = 0.57s
Now considering horizontal motion of skateboarder.
We have equation of motion s =ut + 0.5 at²
u = 6.6cos58 = 3.50 m/s
a = 0 m/s²
t = 0.57
Substituting
s =3.5 x 0.57 + 0.5 x 0 x 0.57²
s = 2 m
When he reaches maximum height he is 2 m far from end of the ramp.
The highest point reached by the skateboarder is 1.612 meters above the ground. When the skateboarder reaches the highest point, the horizontal distance from this point to the end of the ramp is 3.568 meters.
Given:
Initial velocity (v₀) = 6.6 m/s
Launch angle (θ) = 58°
Height of the ramp (h) = 1.2 m
Acceleration due to gravity (g) = 9.8 m/s²
(a) To find the maximum height reached by the skateboarder:
Δy = v₀y² / (2g)
v₀y = v₀ × sin(θ)
v₀y = 6.6 × sin(58°)
v₀y = 5.643 m/s
Δy = (5.643 )² / (2 × 9.8)
Δy ≈ 1.612 m
Therefore, the highest point reached by the skateboarder is 1.612 meters above the ground.
(b) The time of flight can be calculated using the equation:
t = 2 × v₀y / g
t = 2 × 5.643 / 9.8
t = 1.153 s
Δx = v₀x × t
First, we need to find the initial horizontal velocity (v₀x):
v₀x = v₀ × cos(θ)
v₀x = 6.6 × cos(58°)
v₀x = 3.099 m/s
Δx = 3.099 * 1.153
Δx = 3.568 m
Therefore, when the skateboarder reaches the highest point, the horizontal distance from this point to the end of the ramp is 3.568 meters.
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Compute the diameter of a square link subjected to a compres- sive load of 27,000 lbs. Modulus of elasticity 30 x 106 psi. Proportionality limit 38,000 psi, working stress - 7000 psi, length of the link 55 in.
Answer:
The diameter of a square link is 0.0233 inch.
Explanation:
Given that,
Load = 27000 lbs
Modulus of elasticity [tex]E= 30\times10^{6}\ psi[/tex]
Working stress [tex]\sigma=7000\ psi[/tex]
length l = 55 in
We need to calculate the diameter of a square link
Using formula of stress
[tex] \sigma=\dfrac{Force}{Area}[/tex]
[tex]7000=\dfrac{27000}{\pi\times d\times L}[/tex]
Put the value into the formula
[tex]d=\dfrac{27000}{7000\times3.14\times55}[/tex]
[tex]d=0.0223\ inch[/tex]
Hence, The diameter of a square link is 0.0233 inch.
How much heat is required to convert 50 g of ice at -5 degrees Celsius to steam?
Answer:
15435 J
Explanation:
Latent heat of fusion, Lf = 334 J/g
Specific heat of ice, ci = 2.1 J / g C
Latent heat of vaporisation, Lv = 2230 J/g
Specific heat of water, cw = 4.18 J / g C
mass, m = 50 g, T = - 5 degree C
There are following steps
(i) - 5 degree C ice converts into 0 degree C ice
H1 = m x ci x ΔT = 50 x 2.1 x 5 = 525 J
(ii) 0 degree C ice converts into 0 degree C water
H2 = m x Lf = 5 x 334 = 1670 J
(iii) 0 degree C water converts into 100 degree C water
H3 = m x cw x ΔT = 5 x 4.18 x 100 = 2090 J
(iv) 100 degree C water converts into 100 degree C steam
H4 = m x Lv = 5 x 2230 = 11150 J
Total heat required
H = H1 + H2 + H3 + H4
H = 525 + 1670 + 2090 + 11150 = 15435 J
Two banked curves have the same radius. Curve A is banked at 12.7 °, and curve B is banked at an angle of 15.1°. A car can travel around curve A without relying on friction at a speed of 19.1 m/s. At what speed can this car travel around curve B without relying on friction?
The speed of the car on Curve B is obtained by solving for the radius in Curve A's equation, then substituting that into the formula for Curve B. The formula involved is based on principles of circular motion and forces.
Explanation:The subject of this question is Physics, specifically the principles of circular motion and the forces at play within. Given the information from Curve A, we can ascertain that the speed of the car on Curve B can be found using principles of physics. The formula to find the speed at which the car can travel around a banked curve without relying on friction is: v = sqrt[rgtan(Θ)]. Where v is the speed, r is the radius of the curve, g is the acceleration due to gravity, and Θ is the angle of the banked curve.
Since the radius is the same for both curves, and the speed is known for Curve A, we can set it up so: 19.1 = sqrt[r * 9.8 * tan(12.7)]. We then solve for r (the radius), and apply it to Curve B: v = sqrt[r * 9.8 * tan(15.1)]. By substituting in the value of r obtained from the first equation, we can calculate the speed for Curve B.
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To find the speed at which the car can travel around curve B without relying on friction, we can use the same formula but with a banked angle of 15.1°.
Explanation:The speed at which a car can travel around a banked curve without relying on friction can be calculated using the ideal banking angle formula. The formula is given by v = √(g * r * tan(θ)), where v is the speed, g is the acceleration due to gravity, r is the radius of the curve, and θ is the banked angle. In this case, curve A is banked at 12.7° and the car can travel at a speed of 19.1 m/s. To find the speed at which the car can travel around curve B without relying on friction, we can use the same formula but with a banked angle of 15.1°.
Plugging in the values into the formula, v = √(9.8 * r * tan(15.1)). Since the radius is the same for both curves, we can solve for v: 19.1 = √(9.8 * r * tan(12.7))
Solving the equation for v, we find that the car can travel around curve B without relying on friction at a speed of approximately 21.2 m/s.
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The three-dimensional motion of a particle on the surface of a right circular cylinder is described by the relations r = 2 (m) θ = πt (rad) z = sin24θ (m) Compute the velocity and acceleration of the particle at t=5 s.
Answer:
[tex]V_{rex}=75.65m/s[/tex] and [tex]a_{res}=0[/tex] at t=5 secs
Explanation:
We have r =2m
[tex]\therefore \frac{dr}{dt}=0\\\\=>V_{r}=0[/tex]
Similarly
[tex]=>V_{\theta }=\omega r\\\\\omega =\frac{d\theta }{dt}=\frac{d(\pi t)}{dt}=\pi \\\\\therefore V_{\theta }=\pi r=2\pi[/tex]
Similarly
[tex]=>V_{z }=\frac{dz}{dt}\\\\V_{z}=\frac{dsin(24\pi t)}{dt}\\\\V_{z}=24\pi cos(24\pi t)[/tex]
Hence
at t =5s [tex]V_{\theta}=2\pi m/s[/tex]
[tex]V_{z}=24\pi cos(120\pi)[/tex]
[tex]V_{z}=24\pi m/s[/tex]
[tex]V_{res}=\sqrt{V_{\theta }^{2}+V_{z}^{2}}[/tex]
Applying values we get
[tex]V_{res}=75.65m/s[/tex]
Similarly
[tex]a_{\theta }=\frac{dV_{\theta }}{dt}=\frac{d(2\pi) }{dt}=0\\\\a_{z}=\frac{d^{2}(sin(24\pi t))}{dt^{2}}\\\\a_{z}=-24^{2}\pi^{2}sin(24\pi t)\\\\\therefore t=5\\a_{z}=0[/tex]
A 1 cm^3 block with a density of 0.92 g/cm^3 is floating in a container of water (d =1g/ cm^3). You may ignore any air pressure throughout this problem. What buoyant force is necessary to keep the block from sinking?
Answer:
980 dyne
Explanation:
Volume = 1 cm^3, d = 0.92 g / cm^3, D = 1 g/cm^3
In the equilibrium condition, the buoyant force is equal to the weight of the block.
Buoyant force = Volume of block x density of water x g
Buoyant force = 1 x 1 x 980 = 980 dyne
A 1kg ball is dropped (from rest) 100m onto a spring with spring constant 125N/m. How much does the spring compress?
Answer:
3.95 m
Explanation:
m = 1 kg, h = 100 m, k = 125 N/m
Let the spring is compressed by y.
Use the conservation of energy
potential energy of the mass is equal to the energy stored in the spring
m x g x h = 1/2 x ky^2
1 x 9.8 x 100 = 0.5 x 125 x y^2
y^2 = 15.68
y = 3.95 m