A horse is lifting a 500 pound crate by moving to the right at a constant speed

Question

A horse is lifting a 500 pound crate by moving to the right at a constant speed v0 = 3ft/s. Observing that B is fixed and letting h = 6ft and l= 14ft, determine the tension in the rope when the horizontal distance d between B and point A on the horse is 10 ft. The constant speed of the horse does not imply that the acceleration of the crate is zero.

Extra Notes to clarify picture: the height of the horse is h=6ft, Point B is the top pulley and it is fixed, Point A is on the horses neck, l=14 ft is the distance from the bottom to the top, and distance d=10 ft is from point B to point A horizontally or from the top pulley to the horses back(not the diagonal distance), the arrow above the horses head is V0=3 ft/sec.

Explanation / Answer

L rope = sqrt(d^2 + (l-h)^2)

only d changes in time

vrope = 1/2*(d^2 + (l-h)^2)^(-1/2) * 2 d v

vrope = d v*(d^2 + (l-h)^2)^(-1/2)

arope = v^2*(d^2 + (l-h)^2)^(-1/2) -1/2*(d^2 + (l-h)^2)^(-3/2)*2 d v

=v^2*(d^2 + (l-h)^2)^(-1/2)-d*v*(d^2 + (l-h)^2)^(-3/2)

= 3^2* (10^2 + 8^2)^(-1/2) - 10*3*(10^2+8^2)^(-3/2)

=0.688

free body diagram on weight

2 T - m g = m a

2 T - 500 = (500/32)*0.688

T=255.38 N

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