Answer:
1.5g/cm³
Explanation:
Given parameters:
Initial volume of the liquid = 30cm³
Final volume of the liquid = 50cm³
Mass of the liquid = 30g
Unknown:
Density of the liquid = ?
Solution:
Density is the mass per unit volume of a substance.
Density =
volume of the liquid = final volume - initial volume = 50cm³ - 30cm³
volume of the liquid = 20cm³
Density = = 1.5g/cm³
We are asked to determine the force required by the neck muscle in order to keep the head in equilibrium. To do that we will add the torques produced by the muscle force and the weight of the head. We will use torque in the clockwise direction to be negative, therefore, we have:
Since we want to determine the forces when the system is at equilibrium this means that the total sum of torque is zero:
Now, we solve for the force of the muscle. First, we add the torque of the weight to both sides:
Now, we divide by the distance of the muscle:
Now, we substitute the values:
Now, we solve the operations:
Therefore, the force exerted by the muscles is 23.53 Newtons.
Part B. To determine the force on the pivot we will add the forces we add the vertical forces:
Since there is no vertical movement the sum of vertical forces is zero:
Now, we add the force of the muscle and the weight to both sides to solve for the force on the pivot:
Now, we plug in the values:
Solving the operations:
Therefore, the force is 73.53 Newtons.
