Physics Tension Problem

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 3 kg box is pushed on a surface with a force of F = 15 N. The coefficient of static friction, $\mu_s$ is 0.3, and the coefficient of kinetic friction, $\mu_k$ is 0.1.

A. Does the box move?

B. If it does move, calculate the acceleration of the box.

A M$_1$ = 5 kg box rests on a table and is connected to a second box of mass M$_2$ = 10 kg via a rope that hangs over a frictionless pulley as shown. The coefficient of friction, $\mu$ is 0.2, Use free body diagrams to answer the following:

B. What is the tension in the rope?