# Frictionless Pulley Problem

Two boxes with masses 17 kg and 15 kg are connected by a light string that passes over a frictionless pulley of negligible mass as shown in the figure below. The surfaces of the planes are frictionless. The blocks are released from rest. T1 and T2 are the tensions in the strings. Which of the following statements is correct?

In this problem, two boxes with masses of 17 kg and 15 kg are connected by a light string over a frictionless pulley, but unlike the typical setup where the masses hang vertically, these boxes rest on a double inclined plane. The angles of the inclined planes play a crucial role in determining the motion of the boxes, as the gravitational force acting on each mass is divided into components along and perpendicular to the plane's surface.

The component of the gravitational force that pulls the boxes down the incline depends on the angle of each plane, with the force along the incline being calculated as m⋅g⋅sin(θ), where m is the mass, g is the acceleration due to gravity, and θ is the angle of the incline. The interplay between these forces determines whether the system accelerates, remains stationary, or reaches equilibrium. Understanding this distribution of forces is key to analyzing the motion of the boxes, as well as calculating tension in the string and acceleration of the masses.

## Related Problems

As shown in the figure, two blocks with masses m and M (M>m) are pushed by a force F in both Case I and Case II. The surface is horizontal and frictionless. Let R1 be the force that m exerts on M in Case I and RII be the force that m exerts on M in Case II. Which of the following statements is true?

An Object with mass m and initial velocity v is brought to rest by a constant force F acting for a time t and through a distance d. Possible expressions for the magnitude of the force F are: i. $\frac{mv^2}{2d}$ ii. $\frac{2md}{t^2}$ iii. $\frac{mv}{t}$

ii only

iii only

i and ii only

ii and iii only

i, ii, and iii

A toy car of mass 6 kg moving in a straight path, experiences a net force given by the function F = -3t. At time t=0, the car has a velocity of 4 m/s in the positive direction and is located +8 m from the origin. The car will come instantaneously to rest at time t equal to

2/3 s

sqrt( 4/3 ) s

sqrt( 8/3 ) s

sqrt( 8) s

4 s

A block of mass M1 on a horizontal table is connected to a hanging block of mass M2 by a string that passes over a pulley, as shown in the figure below. The acceleration of the blocks is 0.6g. Assume that friction and the mass of the string are negligible. The tension T in the string is