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?

To answer these questions, we can use the principles of work, energy, and heat. Let's break down each question and explain how to find the answers.

1. How far does the golden tub slide?
To find the distance the bathtub slides, we need to use the concept of work done against friction. The work done by friction is given by the equation W = μmgd, where μ is the coefficient of friction, m is the mass of the bathtub, g is the acceleration due to gravity, and d is the distance.

Since the work done by friction is equal to the change in kinetic energy (all of which is converted to heat in this case), we have W = ΔKE. The kinetic energy can be calculated using the equation KE = 0.5mv^2, where m is the mass of the bathtub and v is the velocity.

Therefore, we can equate the work done by friction to the change in kinetic energy: μmgd = 0.5mv^2. By rearranging the equation, we can solve for d: d = (0.5mv^2) / (μmg).

Now, substituting the given values, we have d = (0.5 * 250 kg * (9 m/s)^2) / (0.59 * 250 kg * 9.8 m/s^2). After calculating this expression, you will find the distance the bathtub slides.

2. What is the change in the tub's temperature if the specific heat of gold is 129 J/kg°C?
To find the change in temperature (ΔT), we can use the equation Q = mcΔT, where Q is the heat transferred, m is the mass of the bathtub, c is the specific heat of gold, and ΔT is the change in temperature.

In this case, the heat transferred (Q) is the same as the work done against friction (W) since all the kinetic energy is converted into heat. Therefore, Q = W = μmgd.

Now, we can substitute Q, m, and c into the equation Q = mcΔT to solve for ΔT: μmgd = mcΔT. Rearranging the equation, we have ΔT = (μmgd) / (mc).

By substituting the given values, we can calculate ΔT using the equation ΔT = (0.59 * 250 kg * distance) / (250 kg * 129 J/kg°C).

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 find the energy required to increase the temperature, we can use the equation Q = mcΔT, where Q is the heat transferred, m is the mass of the bathtub, c is the specific heat of gold, and ΔT is the change in temperature.

In this case, we need to find the heat transferred (Q). Substituting the given values into the equation Q = mcΔT, we have Q = (250 kg * 129 J/kg°C) * (27°C - 25°C). Calculating this expression will give you the energy required to increase the bathtub's temperature from 25°C to 27°C.