Physics help. what are the steps to solving the following problems?
Attack on the ice fortress! A comic book villain has taken shelter in an ice fortress in an attempt to hide from the Avengers. Apparently, though, only the Hulk and some guy with a cannon are available to try to extract the bad guy. The walls of the ice fortress are 0.50m thick, and the tensile strength of ice at 0°C is 1.7 x 106 Pa.
a) If the Hulk's fist has a diameter of 6.0 x 101 cm, with how much force will he need to punch the ice wall to make a fist-sized hole? Assume that his fist is a circle where it makes contact with the wall.
b) We fire four iron cannonballs that make it through the wall, but come to a complete stop upon doing so. The cannonballs land in a very small reservoir of water. The cannonballs are heated before being shot and are still at 182°C when they land in 4.00 liters of water that is at 0.0°C. The cannonballs are 15.2 cm in diameter. Do the cannonballs provide enough heat to turn the water into steam? If so, how much steam is produced (in kg)? If not, what is the final temperature of the water and cannonballs?
(Possibly useful information: density of iron, 7.86 x 103 kg/m3; density of water, 1.00 x 103 kg/m3 ; specific heat of water, 4186 J/kg•°C; specific heat of iron, 448 J/kg•°C; latent heat of fusion of water,
2.26 x 106 J/kg)
c) What is the buoyant force on any one of the four cannonballs if it is completely submerged in water? The values you need to solve this are given earlier in the problem.
To solve each of these problems, we can follow a general step-by-step approach:
a) Finding the force needed to punch the ice wall:
1. Determine the area of contact between Hulk's fist and the ice wall. This can be found using the formula for the area of a circle: A = πr^2, where r is the radius of the fist.
2. Calculate the force required by using the formula for pressure: P = F/A. Since pressure is defined as force per unit area, we can rearrange the formula to find the force: F = P * A. Here, P is the tensile strength of ice and A is the area of contact.
b) Determining if the cannonballs provide enough heat to turn water into steam:
1. Calculate the initial heat energy of the iron cannonballs. This can be done using the formula Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
2. Calculate the heat energy required to raise the temperature of the water to the final temperature using the same formula as above.
3. Calculate the heat energy required to change the water to steam using the formula Q = mL, where Q is the heat energy, m is the mass of water, and L is the latent heat of fusion.
4. Compare the total heat energy of the cannonballs with the heat energy required for each process to determine if enough heat is provided.
c) Finding the buoyant force on a submerged cannonball:
1. Calculate the volume of the cannonball using the formula V = (4/3)πr^3, where r is the radius of the cannonball.
2. Find the weight of the cannonball using the formula W = mg, where m is the mass of the cannonball and g is the acceleration due to gravity.
3. Calculate the buoyant force using the formula F_buoyant = ρ_fluid * V * g, where ρ_fluid is the density of the fluid (water in this case), V is the volume of the submerged part of the cannonball, and g is the acceleration due to gravity.
By following these step-by-step approaches, you should be able to solve each of the given problems.