For the following exercises, show that the following vector fields ate conservative by using a computer. Calculate ∫ c F . d r for the given curve 139. The mass of Earth is approximately 6 × 10 2 7 g and that of the Sun is 330,000 times as much. The gravitational constant is 6.7 × 10- 8 cm 3 /s 2 g. The distance of Earth from the Sun is about 1 .5 × 10 1 2 cm. Compute, approximately, the work necessary to increase the distance of Earth from the Sun by 1 cm.
For the following exercises, show that the following vector fields ate conservative by using a computer. Calculate ∫ c F . d r for the given curve 139. The mass of Earth is approximately 6 × 10 2 7 g and that of the Sun is 330,000 times as much. The gravitational constant is 6.7 × 10- 8 cm 3 /s 2 g. The distance of Earth from the Sun is about 1 .5 × 10 1 2 cm. Compute, approximately, the work necessary to increase the distance of Earth from the Sun by 1 cm.
For the following exercises, show that the following vector fields ate conservative by using a computer. Calculate
∫
c
F
.
d
r
for the given curve
139. The mass of Earth is approximately 6 × 1027 g and that of the Sun is 330,000 times as much. The gravitational constant is 6.7 × 10-8cm3/s2 g. The distance of Earth from the Sun is about 1 .5 × 1012 cm. Compute, approximately, the work necessary to increase the distance of Earth from the Sun by 1 cm.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
A basket of flowers of mass 3 kg is placed on a flat grassy slope that makes an angle θ with the horizontal. The coefficient of static friction between the basket and the slope is 0.45 and the basket is on the point of slipping down the slope.
Model the basket of flowers as a particle and the grassy slope as a plane. Take the magnitude of the acceleration due to gravity, g, to be 9.8 m s−2
Express the forces in component form, in terms of θ and unknown magnitudes where appropriate. Write down the equilibrium condition for the basket and hence show that tan θ = 0.45. Determine the angle, in degrees, that the slope makes with the horizontal.
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