Question

A man is dragging a box of mass "m" by using a rope which rests on his shoulder as he accelerates forward along with the box. Assume that the rope is nearly massless and unstretchable and makes a constant angle of " Θ " with the horizontal. The coefficient of kinetic friction between the box and the ground is "u"

A.) What is the maximum allowed tension such that the box doesn't lose contact with the ground

B.) Assume that the value of Tension is "T" and is less than the maximum allowed tension. Determine the distance travelled by the mass if it started from rest and gained a speed of Vf.

Show all work please for A & B. Thank you!

Answer 1

a)

for remained in contact,

Ta sin = mg

Ta = mg / sin ​​​​​​

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b)

Acceleration of the sled

m a = T cos - u ( mg - T sin ​​​​​​)

a = ( T cos - u mg + T sin ​​​​​​) / m

using 3rd equation of motion

Vf^2 = 2 a d

d = Vf^2 * m / ( 2* ( T cos - u mg + T sin ​​​​​​))

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