The wavelength of light emitted most strongly by the tungsten filament of the lightbulb, modeled as a black body at a temperature of 2900 K, is approximately 9.997 × \(10^{-7}\) meters, or 999.7 nanometers.
According to Wien's displacement law, the wavelength (λ) at which a black body emits most strongly is given by the equation:
λ_max = b / T
where λ_max is the wavelength at maximum intensity, b is Wien's displacement constant (approximately 2.898 × \(10^{-3}\) m·K), and T is the temperature in Kelvin.
Substituting the given temperature of 2900 K into the equation, we can calculate the wavelength of light emitted most strongly:
λ_max = (2.898 × \(10^{-3}\) m·K) / 2900 K
≈ 9.997 × \(10^{-7}\) m
Therefore, the wavelength of light emitted most strongly by the tungsten filament of the lightbulb, modeled as a black body at a temperature of 2900 K, is approximately 9.997 × \(10^{-7}\) meters, or 999.7 nanometers.
Learn more about temperature here :
brainly.com/question/9094384?
#SPJ11
The temperature of an object is 15 degrees Celsius. What will be its temperature on the Fahrenheit scale? F= (C x 1.8) + 32.
Answer:
59F
Explanation:
Given parameters:
Temperature in °C = 15°C
Unknown:
Temperature in Fahrenheit scale = ?
Solution:
To solve this, we use the conversion equation below;
F = (C x 1.8) + 32
C is the temperature in celcius;
F = (15 x 1.8) + 32 = 59F
(d) A wire Y has the same cross-sectional area as wire X and is made of the same metal. Wire Y
is longer than wire X.
Wire X in the circuit is now replaced by wire Y. Assume that wire Y has the same temperature
as wire X.
State and explain whether the average drift speed of the free electrons in wire Y is greater
than, the same as, or less than that in wire X.
(3)
w]
X]
g
29°C
Answer:
If the potential difference between the ends of the wire are the same then wire Y will experience a smaller drift speed. This is necessary to explain the difference in resistivity.
what is the power of a student that has done a work of 10 joules in 10 seconds
Answer:
1 Watt
Explanation:
P=W/t
P=10/10
P=1 Watt
what is the correct name for a bond between two phosphorus adtoms and three oxygen atoms
Covalent
Explanation:
Covalent Bond
Answer:
diphosphorus trioxide
Explanation:
Verify that each of the following expressions is a total differential, and find its primitive function: pini soclure gniwolloi adi soolava +1 (1) (x² + 2xy-y²)dx + (x²-2xy - y²)dy; (2) (2xcosy - y² sinx) dx + (2ycosx - x² siny) dy. 108
A total differential is an equation in which all the differentials can be integrated independently of each other. To verify that the given expressions are total differentials, we must check if they meet the conditions of being an exact differential function.The given expression is not an exact differential function.
According to the exact differential function, an expression dQ should be equal to the sum of two partial derivatives of the same function. i.e, dQ= dP+ dRA primitive function of an expression is obtained by integrating the given expression partially. Let's solve the given expressions, one by one:
1. Expression : (x² + 2xy-y²)dx + (x²-2xy - y²)dy. Now, we need to find the partial derivatives of the above function with respect to x and y.∂P/∂x = x² + 2xy - y² ∂Q/∂y = x² - 2xy - y².
On verifying, we get:∂P/∂x = ∂Q/∂y.
Hence, the given expression is an exact differential function.
To find the primitive function, we need to integrate any one of the partial derivatives with respect to x and other with respect to y.
∴ P(x,y) = ∫(x² + 2xy - y²)dx = x³/3 + x²y - xy² + C1 and ∴ Q(x,y) = ∫(x² - 2xy - y²)dy = x²y - y³/3 + C2.
Therefore, the primitive function of the expression is: P(x,y) = Q(x,y) = x³/3 + x²y - xy² - y³/3 + C2.
Expression : (2xcosy - y² sinx) dx + (2ycosx - x² siny) dy. Now, we need to find the partial derivatives of the above function with respect to x and y.∂P/∂x = 2cosy ∂Q/∂y = 2ycosx.
On verifying, we get:∂P/∂x ≠ ∂Q/∂y .
Hence, the given expression is not an exact differential function.
Therefore, there does not exist a primitive function for the given expression.
Learn more about primitive function here ;
https://brainly.com/question/31404756
#SPJ11
Prank text my sister, I wanna see her reaction.
(346) 298-3870
Answer:
she is going to be mad dude
HEAT TRANSFER INTO a system from the surroundings is considered a POSITIVE transfer of energy. True or False?
True, heat transfer into a system from the surroundings is considered a positive transfer of energy. This is because the system is gaining energy from its surroundings, causing its internal energy to increase. This can be represented by a positive value for heat transfer (Q) in the equation for the change in internal energy of a system: ΔU = Q - W, where W is the work done by the system. If heat is transferred out of the system and into the surroundings, it would be considered a negative transfer of energy and represented by a negative value for Q.
Two vehicles have a head-on collision. The vehicles essentially stick together and travel a certain distance for 20 seconds before coming to a complete stop. You are able to obtain the mass of both vehicles, the initial velocity for Vehicle A, and the final velocity for both vehicles immediately after the crash. Can you determine the momentum of both vehicles before the collision?
The answer is yes because of conservation of momentum. That is, the momentum before collision is equal to the momentum after collision.
What is Momentum ?Momentum is the product of mass and velocity. It is a vector quantity. And it is measured in Kgm/s
If two vehicles have a head-on collision, the vehicles essentially stick together and travel a certain distance for 20 seconds before coming to a complete stop. The final velocity for both vehicles immediately after the crash can be obtain by using the formula
v = u - at
Where
v = final velocityu = initial velocitya = accelerationt = timeIf you are able to obtain the mass of both vehicles, the initial velocity for Vehicle A, and the final velocity for both vehicles immediately after the crash, then you can determine the momentum of both vehicles before the collision by calculating the momentum of both after the collision because momentum is always conserved.
Or by first calculating the initial velocity for vehicle B by using the formula below
\(M_{1}U_{1} - M_{2}U_{2} = (M_{1} + M_{2} )V\)
where
M1 = mass of the first objectU1 = initial velocity of the first objectM2 = mass of the second objectU2 = initial velocity of the second objectV = common final velocityAfter we obtain initial velocity for vehicle B, we can calculate the momentum of both vehicles before the collision
Therefore, the momentum of both vehicles before the collision can be determined.
Learn more about Momentum here: https://brainly.com/question/25121535
#SPJ1
A 90kg person jumps from a 30m tower into a tub of water with a volume of 5m3 initially at 20°C. Assuming that all of the work done by the person is converted into heat to the water, what is the final temperature of the water?
The final temperature of the water is 21.2658°C.
Explanation:-
To find out the final temperature of the water after a 90 kg person jumps from a 30 m tower into a tub of water with a volume of 5 m³ initially at 20°C,
assuming that all of the work done by the person is converted into heat to the water,
let's follow the steps given below:
First, let's find out the work done by the person.
The work done by the person will be equal to the potential energy of the person just before the jump minus the potential energy of the person just after the jump.
W = PE₁ - PE₂
where W is the work done by the person
PE₁ is the potential energy of the person just before the jump
PE₂ is the potential energy of the person just after the jump
The potential energy of the person just before the jump is given by mgh,
where m is the mass of the person,
g is the acceleration due to gravity,
and h is the height of the tower.
PE₁ = mgh = 90 × 9.8 × 30 = 26,460 J
The potential energy of the person just after the jump is zero.
PE₂ = 0JTherefore, the work done by the person is
W = PE₁ - PE₂ = 26,460 - 0 = 26,460 J
Now, let's find out the heat energy produced in the water.
The heat energy produced in the water is equal to the work done by the person.
Q = W
where Q is the heat energy produced in the water
W is the work done by the person
Q = 26,460 J
Now, let's find out the change in temperature of the water.
The specific heat capacity of water is 4.18 J/g°C.
Therefore, the amount of heat required to raise the temperature of 1 g of water by 1°C is 4.18 J/g.
Also, we know that the density of water is 1000 kg/m³.
Therefore, the mass of water in the tub is given by the product of the density of water and the volume of the tub.
m = ρV = 1000 × 5 = 5000 g
Therefore, the amount of heat required to raise the temperature of the water by ΔT°C is given by
Q = mcΔT
where c is the specific heat capacity of water
Q = mcΔT = 5000 × 4.18 × ΔT = 20,900
ΔTThe heat energy produced in the water is equal to the amount of heat required to raise the temperature of the water by ΔT°C.
Therefore, we can equate the two equations.
Q = 20,900 ΔT26,460 = 20,900 ΔT
ΔT = 1.2658°C
Final temperature of the water = Initial temperature of the water + Change in temperature of the water
= 20°C + 1.2658°C= 21.2658°C
Therefore, the final temperature of the water is 21.2658°C.
Know more about Work done here,
https://brainly.com/question/15829855
#SPJ11
What is the net displacement of the particle between 0 seconds and 80 seconds?
Choices:
A. 160 meters
B. 80 meters
C. 40 meters
D. 20 meters
E. 0 meters
The correct option is D, The net displacement of the particle between 0 seconds and 80 seconds is 20 meters.
Displacement refers to the distance and direction between an initial point and a final point of an object or particle. It is a vector quantity, meaning that it has both magnitude and direction. Displacement can be calculated by subtracting the initial position vector from the final position vector. For example, if an object moves from point A to point B, the displacement vector is the vector that goes from point A to point B.
Displacement is different from distance traveled, which is the total length of the path taken by an object between two points. Displacement takes into account the direction of motion and the final position of the object, while distance traveled does not. Displacement is often used in physics to describe the motion of objects, and is commonly measured in meters or feet.
To learn more about Displacement visit here:
brainly.com/question/30087445
#SPJ4
which is a harmful role of bacteria of bacteria?
Answer:
Harmful bacteria are called pathogenic
Explanation:
Harmful bacteria are called pathogenic bacteria because they cause disease and illnesses like strep throat, staph infections, cholera, tuberculosis, and food poisoning.
A window in a skyscraper has a surface area of 3.50 m^2. Wind rushes by the outside of the window at 17.4 m/s, while inside the air is stationary. What is the DIFFERENCE IN PRESSURE between the inside and outside?
[?] Pa
The difference in the pressure between the inside and outside will be 369.36 N/m²
What is pressure?
The force applied perpendicular to the surface of an item per unit area across which that force is spread is known as pressure.
It is denoted by P. The pressure relative to the ambient pressure is known as gauge pressure.
The given data in the problem is;
dP is the change in the presure=?
Using Bernoulli's Theorem;
\(\rm \rho\frac{V^2_{12}}{2} +P_1= \rho \frac{V^2_{22}}{2} +P_2 \\\\\ P_2-P_1=\rho \frac{v_2^2-v_1^2}{2} \\\\ P_2-P_1= 1.21 \times \frac{17.4^2-0}{2} \\\\ \triangle p=369.36 \ N/m^2\)
Hence, the difference in the pressure between the inside and outside will be 369.36 N/m²
To learn more about the pressure refer to the link;
https://brainly.com/question/356585
#SPJ1
Answer: 195.2802 → 195 for Acellus
Explanation: 0.5*1.29*17.4^2
which of these makes surface mining less risky than underground mining?
Answer:
B
Explanation:
If you really read and dissect every other question they do not make sense
Gravity affects orbits in outer space.
True or False????
calculate the torque procured by the same 75N force when a pipe extends the length of the wrench to 0.5m
Answer: 37.5 N-M
Explanation:
Wheel A of radius ra = 5.2 cm is coupled by belt B to wheel C of radius rc = 28.5 cm. Wheel A increases its angular speed from rest at time t = 0 s at a uniform rate of 5.1 rad/s2. At what time will wheel C reach a rotational speed of 127.0 rev/min, assuming the belt does not slip?
The time at which the wheel C reach a rotational speed of 127.0 rev/min is 2.6 seconds.
What is the time taken for the wheel C to reach the rotational speed?
The time taken for the wheel C to reach the rotational speed is determined by applying principle of angular momentum as shown below.
LA = LC
the angular momentum of wheel A = angular momentum of wheel C
ωf = ωi + αt
where;
ωf is the final angular velocity of the wheel Cωi is the initial angular velocity of the wheel Cα is the angular acceleration of the wheel Ct is the time taken for the wheel C to reach the final angular velocityThe given parameters;
the initial angular velocity of the wheel C = 0the angular acceleration the wheel C = 5.1 rad/s²the final angular acceleration of wheel C = 127 rev/min = 13.3 rad/s13.3 = 0 + 5.1t
13.3 = 5.1t
t = 13.3/5.1
t = 2.6 seconds
Learn more about rotational speed here: https://brainly.com/question/6860269
#SPJ1
Super Chicken! isn't just any ol' superhero. No, this chicken has a
mass of 81 kg, is 6 feet tall, and can outrun a racehorse at 32 m/s.
What is Super Chicken's! kinetic energy?
One end of a horizontal spring with force constant 76. 0 N/m is attached to a vertical post. A 5. 00-kg can of beans is attached to the other end. The spring is initially neither stretched nor compressed. A constant horizontal force of 51. 0 N is then applied to the can, in the direction away from the post.
What is the speed of the can when the spring is stretched 0. 400 m?
At the instant the spring is stretched 0. 400 m, what is the magnitude of the acceleration of the block?
The required speed of the the can when the spring is stretches is calculated to be 2.39 m/s.
The magnitude of acceleration of the block is calculated to be 4.12 m/s².
The force constant of the spring is given as k = 76 N/m.
Mass of the beans is given as 5 kg.
The constant horizontal force applied is given as 51 N.
The stretching in the spring is given as 0.4 m.
The expression to calculate speed of the block for the stretch in the spring is,
F x - 1/2 k x² = 1/2 m v²
v = √2 (F x - 1/2 k x²)/m
Putting all the values, we have,
v = √2 (51× 0.4 - 1/2× 76 × (0.4)²)/5 = √2 (20.4 - 6.08)/5 = 2.39 m/s.
Thus, the speed of the can for stretch in the spring is 2.39 m/s.
The relation to calculate the magnitude of acceleration of the block is,
a = (F - k x)/m = (51 - 76× 0.4)/5 = 4.12 m/s²
Thus, the magnitude of acceleration is calculated to be 4.12 m/s².
To know more about springs:
https://brainly.com/question/29437144
#SPJ4
The current going through a car starter is 210 A. If the battery maintains 12 V across the motor, how much electrical energy is delivered to the starter in 10.0 s?25 J250 J2.5 102 J2.5 104 J
In order to determine the energy delivered in the given time, first calculate the electric power of the starter, by using the following formula:
\(P=I\cdot V\)where,
I: current = 210 A
V: voltage = 12 V
Replace the previous values of the parameters into the formula for P:
\(P=(210A)(12V)=2520W\)where W means watts.
Now, consider that power is the energy delivered per second. Then, for
10.0 s the energy delivered is:
\(E=P\cdot t=(2520W)(10.0s)=25200J\approx2.5\cdot10^4J\)Hence, the energy delivered by the starter is approximately 2.5*10^4 J
What is the answer for the first part of a? In kN
We are asked to determine the magnitude of the force that acts parallel to the nail. To do that we will add the torque that acts on the point of contact. First, we draw a free-body diagram of the situation:
We have decomposed the force of the nail into its horizontal and vertical components. The horizontal component does no torque since there is no distance parallel to the force to the point of contact.
Now, we add the torques. We consider counterclockwise as positive:
\(\Sigma T=-(30cm)F+(5cm)(R_y)\)Since we consider the moment before there is no angular acceleration the sum of torques adds up to zero:
\(-(30cm)F+(5cm)(R_y)=0\)Now, we determine the value of Ry as a function of "R" using the trigonometric function cosine:
\(\cos \theta=\frac{R_y}{R}\)Now, we multiply both sides by "R":
\(R\cos \theta=R_y\)Now, we substitute in the sum of torques:
\(-(30cm)F+(5cm)(R\cos \theta_{})=0\)Now, we solve for "R". First, we add "30F" to both sides:
\((5cm)(R\cos \theta)=(30cm)F\)Now, we divide both sides by 5cm:
\((R\cos \theta)=\frac{(30cm)F}{5cm}\)Now, we divide both sides by cosine:
\(R=\frac{(30cm)F}{5cm\cos \theta}\)Now, we substitute the values:
\(R=\frac{(30cm)(155N)}{(5cm)\cos 26.9}\)Solving the operations:
\(R=1042.8N\)Therefore, the force on the nail is 1042.8 Newtons.
what do you think is a key difference between living on earth and in space? click on the pictures to find out more
One key difference between living on earth and in space is the effect of gravity on the human body. On earth, gravity provides a constant force that keeps our bones and muscles strong. In space, however, gravity is much weaker and astronauts experience weightlessness. This can lead to various health problems, such as bone loss, muscle atrophy, and fluid shifts. Therefore, astronauts need to exercise regularly and follow a balanced diet to maintain their physical and mental well-being.
About GravityGravity is a natural phenomenon whereby everything that has mass or energy in the universe—including planets, stars, galaxies, and even light—attracts one another.
Learn More About Gravity at https://brainly.com/question/940770
#SPJ11
A change of position is called
o distance
O velocity
O speed
O displacement
What accommodations can be made for people with impaired vision?
A 61.7 kg carpenter at a construction site plans to swing in a circular arc from one roof top to an adjacent roof at the end of a 11.5 meter rope suspended from a crane boom. if her wiry arms, toughened by years of driving spikes with a no. 22 framing hammer, are capable of exerting 1229 n of force on the rope, what is the maximum speed that she can tolerate at the low point of her swing?
At the lowest point of her swing, she can withstand a maximum speed of 10.78 m/s.
Given that,
Mass of the carpenter = 61.7 kg
Length of the rope = 11.5 m
Capable force = 1229 N
Centripetal force acting on the body,
F = mv²/r = (61.7× v²)/11.5 = 5.37 v²
Gravitational force acting on her is
F = m × g = 61.7 × 9.81 = 605.28 N
By summing up gravitational and centripetal forces to get the total available force,
5.37 v² + 605.28 = 1229
5.37 v² = 623.72
v² = 116.15
v = 10.78 m/s
Hence, the maximum speed at the low point of her swing is 10.78 m/s.
To know more about speed:
https://brainly.com/question/29794453
#SPJ4
What type of system would allow light and air to enter and exit? A. Connected
B. Closed C. Isolated D. Open
Answer:
An open system.
Explanation:
An isolated system allows the exchange of neither energy nor matter with the surroundings. A closed system allows the exchange of energy, but not matter. An open system allows the exchange of both energy and matter.
Notice that in this question, light (electromagnetic wave) is a form of energy. The entry and exit of light allows this system to exchange energy with its surroundings- just as how the earth receives energy from the sun. Additionally, this system could exchange energy with its surroundings through the exchange of matter (in particular, air) with its surroundings.
Thus, the system in this question is an open system.
When you serve the ball, if the ball does not land in the opposite side rectangle this is called a ______. question 2 options: fault miss volley foul
Answer:
its called a fault
Explanation:
Its when u mess up
Matching Scientists with Atomic Models
Which scientist and atomic model are correctly matched?
Bohr – plum pudding
Thomson – electron cloud surrounds nucleus
Rutherford – plum pudding
Schrödinger – electron cloud surrounds nucleus
The correct answer is option 4 Schrödinger.
The distribution of electrons within Thomson's model's positively charged region of space quickly earned it the informal moniker "plum pudding," since it reminded many scientists of the raisins—then known as "plums"—found in the traditional English delicacy plum pudding.
Erwin Schrodinger's Electron Cloud Model. With the help of this concept, electrons were no longer pictured as being in a fixed orbit around a central nucleus.
In a series of publications published in 1926, Schrödinger addressed the problem of wave functions and electrons. He utilised mathematical calculations to quantify the probability of finding an electron in a particular position in addition to describing what would later be known as the Schrodinger equation, a partial differential equation that explains how the quantum state of a quantum system varies with time.
This served as the foundation for the Schrodinger equation and the Electron Cloud (quantum mechanical) Model, respectively. The Electron Cloud Model, based on quantum theory, which holds that all matter has qualities related to a wave function, is different from the Bohr Model in that it does not specify the precise route of an electron.
To learn more about electron cloud surrounds nucleus refer the link:
https://brainly.com/question/75389
#SPJ9
Talia is in a road trip with some friends. I. The frist 2 hours they travel 100 miles then they hit traffic and go only 30 miles in the next hour the last out of the round trip they drive 75 miles calculate the evergreen speed of the car
Correct question is;
Talia is on a road trip with some friends. in the first 2 hours, they travel 100 miles. then they hit traffic and go only 30 miles in the next hour. the last hour of their trip, they drive 75 miles. calculate the average speed of talia’s car during the trip. give your answer to the nearest whole number.
Answer:
Average speed ≈ 51 mi/hr
Explanation:
Total distance travelled by Talia = 100 + 30 + 75 = 205 miles
Total time taken by Talia = 2 + 1 + 1 = 4 hours.
Now, formula for average speed is;
Average speed = Total distance/total time
Thus;
Average speed of talia = 205/4
Average speed of talia ≈ 51 mi/hr
Two blocks are connected vertically by a string over a massless, frictionless pulley. If one block has a mass 13.6 kg and the other has a mass of 4.5 kg, what is the magnitude of the acceleration of each block
The magnitude of the acceleration of each block, if two blocks are connected vertically by a string over a massless, frictionless pulley, and one block, has a mass of 13.6 kg and the other has a mass of 4.5 kg is 3.2 m/s².
The acceleration of both blocks is the same magnitude (as they are connected together by the string).
How to find the magnitude of acceleration? To find the magnitude of the acceleration of the blocks, we can use the following steps:
Step 1: Find the gravitational force acting on both blocks.
We know that the gravitational force acting on an object is given by
F = m*g
where m is the mass of the object and g is the acceleration due to gravity.
Step 2: Identify the direction of acceleration for each block.
Step 3: Use Newton's second law of motion to determine the acceleration of each block.
Step 4: Calculate the magnitude of acceleration.
Step 1: Find the gravitational force acting on both blocks.
The gravitational force acting on the larger block (13.6 kg) is
F₁ = m₁*g
= 13.6 kg * 9.81 m/s²
= 133.416 N
The gravitational force acting on the smaller block (4.5 kg) is
F₂ = m₂*g
= 4.5 kg * 9.81 m/s²
= 44.145 N
Step 2: Identify the direction of acceleration for each block.
The direction of acceleration for the larger block is downwards because the gravitational force is greater than the tension in the string.
The direction of acceleration for the smaller block is upwards because the tension in the string is greater than the gravitational force.
Step 3: Use Newton's second law of motion to determine the acceleration of each block.
The net force acting on each block is given by
F = m*a
Where F is the net force, m is the mass, and a is the acceleration.
FOR THE LARGER BLOCK: The net force acting on the larger block is given by:
F - T = m₁*a
where T is the tension in the string.
Substituting the values, we get:
133.416 N - T = 13.6 kg * a------(1)
FOR THE SMALLER BLOCK: The net force acting on the smaller block is given by:
T - F = m₂*a
Substituting the values, we get:
T - 44.145 N = 4.5 kg * a----- (2)
Step 4: Calculate the magnitude of acceleration.
To find the magnitude of acceleration, we need to solve the above two equations simultaneously.
133.416 N - T = 13.6 kg * aT - 44.145 N
= 4.5 kg * a
Adding the two equations, we get:
89.271 N = 18.1 kg * a
So, the magnitude of the acceleration of both blocks is:
a = 89.271 N / 18.1 kg
= 4.93 m/s²
Now, we know the acceleration of both blocks is the same magnitude (as they are connected together by the string).
Therefore, the magnitude of the acceleration of each block is 3.2 m/s² (approx).
To know more about gravitational force visit:
https://brainly.com/question/32609171
#SPJ11
In an experiment, 120 g of ice at 0 °C is to be melted. The specific latent heat of
ice is 340 J/g. Assume that all the energy from the heater will be used to melt
the ice.
Q1) Calculate the expected time for which the 60 W heater is switched on.
Answer:
\(680\; \rm s\).
Explanation:
Start by finding the total amount of energy required for melting that much ice.
\(\begin{aligned}&\text{Energy required for melting ice sample} \\ &= \text{Mass of Ice} \times \text{Specific Latent Heat of Ice} \\ &= 120\; \rm g \times 340\; \rm J \cdot g^{-1} = 4.08 \times 10^{4}\; \rm J \end{aligned}\).
Hence, the heater would need to supply (at least) \(4.08 \times 10^{4}\; \rm J\) of energy.
The power of the heater is \(60\; \rm W\), which is equivalent to \(60\; \rm J \cdot s^{-1}\), In other words, the heater is rated to supply \(60\; \rm J\) of energy every second.
Amount of time it takes for the heater to supply \(4.08 \times 10^{4}\; \rm J\) at \(60\; \rm J \cdot s^{-1}\):
\(\begin{aligned}\frac{4.08 \times 10^{4}\; \rm J}{60\; \rm J \cdot s^{-1}} = 680\; \rm s\end{aligned}\).
Hence, it would take \(680\; \rm s\) for the heater to melt the ice if the heater is insulated, and all the energy from the heater went to the ice.