A bank robber is pulling a safe weighing 1000 N up an incline plane onto a truck

Question

A bank robber is pulling a safe weighing 1000 N up an incline plane onto a truck at constant velocity. The plane is inclined at an angle of 30 ? with respect to the horizontal. The force F shown below is applied to the safe at an angle of 37 ? with respect to the surface of the inclineed plane. The coefficient of kinetic (sliding) friction between the safe and the plane is ?k = 0.25

a) (5 pts) Draw a diagram showing all the forces on the safe.

b) (5 pts) Using the x-y coordinate system in the figure write the x-component equation of Newton's Law. (put all known numbers into the equations) _________________________________

c)(5 pts) Using the x-y coordinate system in the figure write the y-component equation of Newton's Law. (put all known numbers into the equations) ___________________________________

d) (5 pts)Calculate the magnitude of the force required to pull the safe up the incline at a constant velocity? ____________________

Explanation / Answer

the forces acting on the safe
F from the robber F(x)= +F cos37º, F(y)= +Fsin37º
W ........................ W(x)= -Wcos30 , W(y)= -Wsin30
F(N) _|_ the slope, F(N)= W(y)
anf F(f) = µ F(N)= - µ mgsin30

since Ff = µmg when the floor is flat, when there is a slope then the F normal will offset the x component of the weight.

draw the W vector, from there draw the rectangle for x and y components of the W vector
use the trig laws, sine and cosine to figure out Wx and Wy with respect to W
since F normal now offsets the part of the W component opposite F normal, which is the Wy in the (-) direction, F normal by mgsin30

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