Box A is initially at rest on a conveyor belt when the belt is suddenly started

Question

Box A is initially at rest on a conveyor belt when the belt is suddenly started in a downward direction so that slipping occurs between the belt and the box. Knowing that the coefficient of kinetic friction between the belt and the box is u_k = 0.3, determine the initial acceleration of the box. As a first approximation to the analysis of a space flight from the earth to Mars, assume the orbits of the earth and Mars are circular and coplanar. The mean distances from the sun to the Earth and to Mars 6 149.6 times 10^6 km and 227.8 times 10^6 km, respectively. Describe the process needed to bring a spacecraft back home to earth using an elliptical transfer orbit knowing that the mass of the sun is 3 332.8 10 times 10^3 times the mass of the earth. Velocity needed to match the orbit of Mars = Velocity of spacecraft as it approaches Earth = Velocity needed to match the orbit of the earth = Procedure to bring spacecraft from Mars back home to Earth:

Explanation / Answer

3)

u = 0.30

for the initial acceleration

as the maximum acceleration can be

a = g * (sin(theta) + u * cos(theta))

a = 9.8 * (sin(15 degree) + 0.30 * cos(15 degree))

a = 5.37 m/s^2

the initial acceleration of the box is 5.37 m/s^2

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