Question

please help me with those two questions

*35. A large, wooden 250-kg packing crate is placed on a steel ramp with an incline of 37e by a loading rig. (a) Will the crate slide down the ramp? (See Table 7.1.) How much force must workers apply parallel to the ramp surface (b) to get the crate to move or to keep it from mov- ing, and (c) to keep it moving at a constart velocity?

Answer 1

a)

component of gravity acting along the surface = m*g*sin(theta)

= 250*9.8*sin(37)

= 1474 N

limiting value of static friction, fs_max = mue_s*N

= mue_s*m*g*cos(theta)

= 0.05*250*9.8*cos(37)

= 98 N

clearly, 1474 > 98 N

so, the body slides down.

b) The force that must be applied to keep it from moving, F = 1474 - 98

= 1376 N

c) to move with constant velocity, F = m*g*sin(theta) - fk

= m*g*sin(theta) - fk

= m*g*sin(theta) - mue_k*N

= m*g*sin(theta) - mue_k*m*g*cos(theta)

= 250*9.8*sin(37) - 0.03*250*9.8*cos(37)

= 1416 N