Calculation Drawing

During a cardiac stress test, 35 g of blood enters the left ventricle at 20 cm/s and exits 0.20 s later at 48 cm/s. What is the estimated average force on the blood as it moves through the ventricle?

A biomedical engineer is testing an implantable sensor that uses a parallel plate capacitor to detect changes in tissue hydration. The capacitor plates are square, each with a side length of 0.05 m, separated by a distance of 2.0 mm. The device is initially connected to a 60 V battery with only air between the plates (κ = 1). After the battery is disconnected, a technician slides a dielectric slab (κ = 3) halfway into the gap between the plates, filling exactly half the plate area while leaving the other half filled with air. The system can be modeled as two capacitors sharing the same plate separation but different dielectric materials, connected in parallel.

How much additional charge, in coulombs, is stored on the capacitor after the dielectric is inserted compared to before?

Water flows through a rectangular channel that is 0.80 m wide and filled to a depth of 0.50 m. The water surface sits 1.8 m above a reference datum, and flow velocity at this point is 0.60 m/s. The channel then narrows to 0.40 m wide while the depth remains 0.50 m. Assume ideal, incompressible flow with no energy losses. (ρ = 1,000 kg/m³, g = 10 m/s²)

What is the water velocity in the narrow section, and what is the height of the water surface above the reference datum at that point?

A 36 V battery is connected in series with R₁ = 12 Ω. At the junction after R₁, the circuit splits into two parallel branches: one containing R₂ = 18 Ω, and the other containing R₃ = 9 Ω and R₄ = 9 Ω in series with each other.

What is the current through R₂ alone, and what is the power dissipated by R₁?

Two masses are connected by an inextensible string over a frictionless, massless pulley. Mass M₁ = 8 kg hangs on the left and mass M₂ = 5 kg hangs on the right. The system is released from rest. After M₁ has descended 1.2 m, the string is suddenly cut. (g = 10 m/s²)

What is the velocity of the system just before the string is cut, and how much additional vertical distance does M₁ travel upward after the string is cut before momentarily stopping?