Question

A physics student takes a 5.0-kg pail of water connected on a rope, and swings it in a vertical circle of radius 90.0 cm at a constant speed of 7.0 m/s.
Figure 1 1.2.1 When the pail passes its highest point, what are the magnitude and direction of its acceleration? [5] 1.2.2 When the pail passes its highest point, what is the tension in the rope? [5] 1.3 One day, the air near Earth’s surface at the Polokwane airport has a uniform density of 1.20 kg/m3, and the absolute pressure at ground level is 99.8 kPa. 1.3.1 What force magnitude does the air pressure produce perpendicular to a horizontally oriented surface of area 1.00 m2 [4] 1.3.2 At increasing elevation above ground level, the pressure (choose from: increases; decreases or does not change) [2] 1.3.3 Calculate the absolute pressure at an elevation of 1.00 km above the Polokwane airport that day.

Answer 1

1.2.1

$$a=\frac{v^2}{r}+g=\frac{7^2}{0.9}+9.8=64.2\frac{m}{s^2}$$

Downwards.

 1.2.2

$$T=ma=(5)(64.2)=321\ N$$

1.3.1

$$F=pA=(99800)(1)=99800\ N=99.8 \ kN$$

1.3.2

At increasing elevation above ground level, the pressure decreases.

 1.3.3

$$p'=p-\rho gh=99800-(1.2)(9.8)(1000)=88000\ Pa=88\ kPa$$