Question

Question 1 Figure (a) shows a uniform ramp between two buildings that allows for motion between the buildings due to strong winds. At its left end, it is hinged to the building wall; at its right end, it has a roller that can roll along the building wall. There is no vertical force on the roller from the building, only a horizontal force with magnitude Fh. The horizontal distance between the buildings is D = 4.00 m. The rise of the ramp is h = 0.303 m. A person walks across the ramp from the left. Figure (b) gives Fn as a function of the horizontal distance x of the person from the building at the left. The scale of the Fn axis is set by a = 20 kN and b = 25 kN. What are the masses of (a) the ramp and (b) the man? HZ. 2 x(m) (6) (a) (a) Number Units (b) Number Units

Answer 1

taking moment about the left end, we have

F_h h = mgx + MgL/2

if we compare this with straight-line equation

y = mx + b

F_h = (mg/h) x + MgD / 2h

so,

from graph, intercept = 20 kN = 20000 N

so,

MgD / 2h = 20000

M * 9.8 * 4 / 2 * 0.303 = 20000

M = 309.2 Kg ( mass of ramp)

_____________________________________

Now, from the graph

slope = 25000 - 20000 / 4 = 1250 N/m

so,

mg / h = 1250

m * 9.8 / 0.303 = 1250

m = 38.65 Kg ( mass of the man)