To find the distance between the fulcrum and the mass, we can use the concept of torque. Torque is the rotational equivalent of force and is calculated by multiplying the force by the perpendicular distance from the fulcrum.
In this case, we have a lever of length 2.4 m that is being lifted by a force of 300 N. Let's denote the distance between the fulcrum and the mass as 'x'.
The torque on the lever is given by the equation:
Torque = Force × Distance
In this case, the torque exerted by the force is equal to the torque exerted by the mass.
So, we can write the equation as:
300 N × 2.4 m = 120 kg × g × x
where g is the acceleration due to gravity.
Simplifying the equation, we get:
720 N·m = 120 kg × g × x
Now, we know that the value of g is approximately 9.8 m/s².
Substituting this value in the equation, we get:
720 N·m = 120 kg × 9.8 m/s² × x
Simplifying further, we have:
720 N·m = 1176 kg·m²/s² × x
Dividing both sides of the equation by 1176 kg·m²/s², we get:
0.6122 = x
Therefore, the distance between the fulcrum and the mass (x) is approximately 0.6122 meters.
To convert this to centimeters, we multiply by 100:
Distance in centimeters = 0.6122 m × 100 cm/m
Distance in centimeters = 61.22 cm
Therefore, the correct answer is not given in the options provided. The actual distance between the fulcrum and the mass is approximately 61.22 cm.