1) A small dense object is suspended from the rear view mirror in a car by a lightweight fiber. As the car is accelerating at 1.90 m/s 2, what angle does the string make with the vertical?

2) A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised bottle to a needle inserted in the vein. The inside diameter of the 25 mm long needle is 0.80 mm and the required flow rate is 2.0 cm^3 of blood per minute. How high should the bottle be placed above the needle? Assume the blood pressure is 78 torr above atmospheric pressure. (Viscosity of blood = 4 x 10^-3 Pas, density of blood = 1.05 x 10^3 kg/m^3)

part 1

I think it might be sin-1(a/m)=11.18 degrees rounded.

nah its tan-1(a/m)

sorry if you r not smart enough to answer get a baby and raise him well then eat in kfc

1) To determine the angle the string makes with the vertical, we can use basic trigonometry. Let's consider the forces acting on the suspended object. There are two forces: the tension force in the string (T) and the weight force acting vertically downward (mg).

Since the car is accelerating, there is an additional force acting on the object in the direction opposite to the acceleration (ma). This force is transmitted through the string and creates an additional angle.

To find this angle, we can break down the forces into their vertical and horizontal components. The vertical component of tension (T_v) is equal to the weight force (mg), while the horizontal component of tension (T_h) is equal to ma.

Using the given acceleration (a = 1.90 m/s^2) and the mass of the object (m), we can compute T_h using the equation T_h = ma.

Then, we can find the angle θ using the equation tan(θ) = T_v/T_h.

2) For this problem, we need to apply principles of fluid dynamics. The flow rate, Q, can be calculated using the equation Q = A * v, where A is the cross-sectional area of the needle and v is the velocity of blood flow.

First, we need to convert the flow rate from cm^3/min to m^3/s. Then, we can calculate the velocity of blood flow by dividing the flow rate by the cross-sectional area of the needle.

Given the inside diameter of the needle (0.80 mm), we can calculate the cross-sectional area (A) using the equation A = π * (d/2)^2.

Next, we need to determine the pressure difference required to achieve the desired flow rate. This can be calculated using the equation ΔP = (Q * η) / (A * l), where ΔP is the pressure difference, η is the viscosity of blood, A is the cross-sectional area of the needle, and l is the length of the blood-filled tube (25 mm).

Finally, we need to determine the height of the bottle above the needle to establish the required pressure difference. We can use the equation ΔP = ρ * g * h, where ρ is the density of blood, g is the acceleration due to gravity, and h is the height.

By substituting the given values for ΔP, ρ, g, and η into the equation, we can solve for h.