Coefficient of Friction 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

Determine the acceleration of the system if M = 10 kg and m = 30 kg and $\theta$ = 30 degrees. Determine the tension in the rope as well.

Determine the acceleration of the system if M = 5 kg and m = 10 kg and $\theta$ = 30 degrees. There is also a coefficient of friction, $\mu$ = 0.2. Use a free body diagram to determine the tension in the rope and the acceleration of the system.