2 Here is a block that starts out with a speed of 3 ms trave

2.

Here is a block that starts out with a speed of 3 m/s, travels over 1 meter of frictionless surface then 1 meter of rough surface. What is the final speed of the block? What is the acceleration of the block while over the rough patch? How much time does it take the block to traverse the 2 meter? Here is the same block but the patches are in reversed order. What is the final speed of the block? What is the acceleration of the block while over the rough patch? How much time does it take the block to traverse the 2 meter? A block of mass m goes through the following motion. It is pushed by a constant force F up a ramp of angle 0 over a height of h. There is friction between the block and the ramp and the coefficient of kinetic friction is mu k. At the top of the ramp, the block is dropped back down to the original ground level. What is the total work done by the force F? What is the total work done by the friction force? What is the total work done by gravity?

Solution

a)

the expression for the frictional force = -umg

the decceleration = f /m

                             = -ug

                            = -0.3 x 9.81 / 1

                            = - 2.94 m/s^2

the speed is calculated as follows:

     v^2 - u^2 = 2ad

    v^2 - 3^2 = 2 x -2.94 x 1

                v = 1.76 m/s

(b)

the acceleration is,

    a = - 2.94 m/s^2

c)

for first one meter, the time is, t1 = d/v = 1/3 = 0.33 s

for last one meter , the time is,

                 v = u + at

            1.76 = 3 0 2.94t2

               t2 = 0.422 m

therefore, the required time:
              t = t1 + t2 = 0.755 s