A large box of mass M is pulled across a horizontal, frictionless surface by a h

Question

A large box of mass M is pulled across a horizontal, frictionless surface by a horizontal rope with tension T. A small box of mass m sits on top of the large box. The coefficients of static and kinetic friction between the two boxes are mu_s, and mu_k., respectively. Find an expression for the maximum tension T_max for which the small box rides on top of the large box without slipping. Express your answer in terms of the variables M, m, mu_s, and appropriate constants. A horizontal rope pulls a 12 kg wood sled across frictionless snow. A 6.0 kg wood box rides on the sled. What is the largest tension force for which the box doesn't slip? Assume that mu_s = 0.50. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

a) Assuming the small box doesn't slip, the tension T accelerates mass M+m according to
T = (M+m)*a
For box m to ride along and not slip, the force of static friction:
Ff_s = m*a
The force of static friction is given by
Ff_s = us*N = us*m*g

We can write an expression for the maximum acceleration
Ff_s = m*a = us*m*g
a = us*g

Using that in the first expression, the max T that avoids slippage is
T = (M+m)*us*g
your mistake was that, you just forget gravity in your exprees

B.

T = (12+6)*0.5*9.81 = 9*9.81 = 88.29 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.