Answer to Question #287382 in Physics for Mateo

Question

A box of mass 5.5kg is resting on a surface and is attached to a hanging 1.0kg bucket by 

lightweight string and a frictionless pulley. The coefficient of static friction between the surface and the box is us=0.40.

a) How many grapes (mgrape =16g) can a student put in the basket without moving the box? T/3

b) When just enough whole grapes have been added to the basket, the system begins to move. If the coefficient of kinetic friction is pk=0.34 between the box and the surface, calculate the

acceleration of the bucket and the tension between the box and bucket. T/4

Answer 1

a) Find the tension required to move the box. The tension is equal for both box and bucket:

$$T=\mu_s Mg=(m+Nm_g)g,\\\space\\ N=\dfrac {\mu_sM-m}{m_g}=75.$$

b) Calculate the acceleration of the bucket and the tension between the box and bucket. Write the forces acting on the box and bucket with grapes by Newton's second law:

$$Ma=T-\mu_kMg,\\ -(m+Nm_g)a=-(m+Nm_g)g+T,\\\space\\ a=8.99\text{ m/s}^2,\\ T=61.6\text{ N}.$$