A gas is confined in a 0.47-m-diameter cylinder by a piston, on which rests a weight. The mass of the piston and weight together is 150 kg. The atmospheric pressure is 101 kPa. (a)What is the force (in Nt) exerted on the gas by the piston, the weight and the atmosphere combined? Neglect friction between the piston and cylinder.

(b) If the friction was not negligible, would the force in part (a) be smaller or larger. Explain.

To find the force exerted on the gas by the piston, weight, and atmosphere combined, we need to consider the different components contributing to the force.

(a) Force exerted by the weight:
The force exerted by the weight can be calculated using the equation:
Force = mass * acceleration due to gravity.

The mass of the piston and weight combined is given as 150 kg. The acceleration due to gravity is approximately 9.8 m/s^2.
So, the force exerted by the weight is:
Force_weight = 150 kg * 9.8 m/s^2.

(b) Force exerted by the atmospheric pressure:
The force exerted by the atmospheric pressure can be calculated by multiplying the pressure by the cross-sectional area of the cylinder, which is the area of a circle with diameter 0.47 m.

The formula for the force exerted by the atmospheric pressure is:
Force_atm = pressure * area.

The atmospheric pressure is given as 101 kPa, which needs to be converted to Newtons per square meter (N/m^2) or Pascals (Pa). There are 1000 Pascals in 1 kPa. So, the atmospheric pressure is:
Pressure = 101 kPa * 1000 = 101000 Pa.

The area of the cylinder can be calculated using the formula for the area of a circle:
Area = π * (radius)^2.
Given the diameter of the cylinder is 0.47 m, the radius is half of that, which is 0.235 m.
So, the area is:
Area = π * (0.235 m)^2.

(c) Force exerted by the piston:
Since there is no friction mentioned in the problem, the force exerted by the piston would be equal to the combined force exerted by the weight and the atmospheric pressure.
Force_piston = Force_weight + Force_atm

Now that we have the components, let's substitute the values and calculate:

Force_weight = 150 kg * 9.8 m/s^2.
Force_atm = 101000 Pa * π * (0.235 m)^2.
Force_piston = Force_weight + Force_atm.

(b) If there was friction present, the force exerted by the piston would be smaller than the force calculated in part (a). This is because friction acts opposite to the direction of motion and resists it. It would require an additional force to overcome friction and maintain the same net force on the piston. Therefore, if friction was not negligible, the force exerted on the gas by the piston, weight, and atmosphere combined would be smaller.