1.) A lawnmower engine claims to provide 18 hp of power and 6.25 ft lb of torque. If this is true, what must be the rotational speed in RPM?

2.) The conversion of the shaft power of a wind turbine to electricity is the function of the generator. Assume it has an efficiency of 0.45. If the wind turns the shaft of a generator at 26.2 rad/s (about 250 RPM) and the generator produces 300 W of electricity, what torque is produced by the wind on the shaft?

1.) To find the rotational speed in RPM, we need to understand the relationship between horsepower (hp), torque (ft lb), and rotational speed (RPM). The equation that relates these variables is:

Power (hp) = (Torque (ft lb) x RPM) / 5252

We are given the power of 18 hp and the torque of 6.25 ft lb. We can rearrange the equation to solve for RPM:

RPM = (Power (hp) x 5252) / Torque (ft lb)

Substituting the given values:

RPM = (18 hp x 5252) / 6.25 ft lb

RPM ≈ 15168 RPM

Therefore, the rotational speed of the lawnmower engine must be approximately 15168 RPM.

2.) To find the torque produced by the wind on the shaft, we can use the equation:

Power (W) = Torque (Nm) x Angular Speed (rad/s)

We are given the power of 300 W and the angular speed of 26.2 rad/s. The equation can be rearranged to solve for torque:

Torque (Nm) = Power (W) / Angular Speed (rad/s)

Substituting the given values:

Torque (Nm) = 300 W / 26.2 rad/s

Torque ≈ 11.45 Nm

Therefore, the torque produced by the wind on the shaft is approximately 11.45 Nm.

1.) To find the rotational speed in RPM, we need to use the relationship between horsepower (hp), torque, and rotational speed.

The formula is:

Power (in hp) = (Torque (in ft lb) * Rotational Speed (in RPM)) / 5252

Given that the lawnmower engine provides 18 hp of power and 6.25 ft lb of torque, we can rearrange the formula to solve for rotational speed:

Rotational Speed (in RPM) = (Power (in hp) * 5252) / Torque (in ft lb)

Substituting the values:

Rotational Speed (in RPM) = (18 * 5252) / 6.25

Simplifying:

Rotational Speed (in RPM) = 15000.48 RPM

Therefore, the rotational speed of the lawnmower engine must be approximately 15000.48 RPM.

2.) To find the torque produced by the wind on the generator shaft, we can use the formula:

Torque = Power / (Rotational Speed * Efficiency)

Given that the generator produces 300 W of electricity, the wind turns the shaft at 26.2 rad/s (about 250 RPM), and the efficiency of the generator is 0.45, we can substitute these values into the formula:

Torque = 300 / (26.2 * 0.45)

Simplifying:

Torque = 300 / 11.79

Therefore, the torque produced by the wind on the generator shaft is approximately 25.46 Nm (Newton meters).