A solid gold bathtub (mass=250 Kg)is pushed along a horizontal cement road (mew=0.59)by criminals. The criminals, in fear of capture, run away and leave the bathtub sliding with a velocity of 9 m/s. Assuming all kinetic energy is converted to heat from frictional work. 1.How far does the golden tub slide?
2.What is the change in the tubs temperature if the specific heat of gold is 129 J/Kg C?
3.How much energy would you have to add to increase the temperature of the bath tub from 25 degrees Celsius to 27 degrees Celsius?
1.
mv²/2=μmgs
s=v²/2μg
2.
mv²/2=Q=cmΔT
ΔT=v²/2c
(c=129000 J/kg•C)
3.
Q=cmΔT= mv²/2
Q1= cmΔT1=cm•2=…
ΔQ=Q1-Q= cm•2- mv²/2 = …
You saved my life Elena. Much appreciated.
To solve these problems, we need to use some concepts from physics. Let's break down each question and find the answers step by step:
1. How far does the golden tub slide?
To determine the distance the golden tub slides, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The work done by friction can be calculated using the formula:
Work = Force of friction × distance
The force of friction can be calculated using the formula:
Force of friction = coefficient of friction × normal force
The normal force in this case is equal to the weight of the golden tub, which can be calculated as:
Normal force = mass × gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s².
Now let's calculate the force of friction:
Force of friction = (0.59) × (250 kg) × (9.8 m/s²)
Next, we'll calculate the work done by friction:
Work = Force of friction × distance
Given that the kinetic energy is converted entirely into heat, the work done by friction is equal to the initial kinetic energy of the tub:
Work = (1/2) × mass × velocity²
Setting the work done by friction equal to the initial kinetic energy, we can solve for the distance:
(0.59) × (250 kg) × (9.8 m/s²) × distance = (1/2) × (250 kg) × (9 m/s)²
Now, we can rearrange the equation and solve for the distance:
distance = [(1/2) × (250 kg) × (9 m/s)²] / [(0.59) × (250 kg) × (9.8 m/s²)]
By plugging the given values into the equation, we can find the distance.
2. What is the change in the tub's temperature if the specific heat of gold is 129 J/kg°C?
To calculate the change in temperature, we need to determine the heat energy generated due to the friction.
The heat energy generated can be calculated using the equation:
Heat energy = Work done by friction
Using the formula from the previous question, we can find the work done by friction. Then, we can calculate the change in temperature using the formula:
Change in temperature = Heat energy / (mass × specific heat)
3. How much energy would you have to add to increase the temperature of the bathtub from 25 degrees Celsius to 27 degrees Celsius?
To calculate the energy required to increase the temperature, we need to determine the heat energy required.
The heat energy required can be calculated using the formula:
Heat energy = (mass × specific heat) × (change in temperature)
Using the given values, we can solve for the energy required to increase the temperature.