Physics Forces: Please help

Question

1. A force of 4N acts on an object of mass 0.5kg which is initially at rest. Calculate the acceleration:

Use the equations of motion to find how far the object travels in 5s:

2. For how long must a force of 120N act on a mass of 50kg to produce a change in velocity from 1.00 to 5.50m/s^-1 if there is a force of 20N opposing the motion?

3. A net force of 20N acts on a 5kg mass for 6s. The original velocity of the mass is 100m/s^-1. Calculate the velocity after 6s if:
 

a) the force is applied in the same direction as that in which the body is moving:

b) the force is applied in the opposite direction to the original motion:

4. A body of a mass of 10kg rests on a smooth inclined plane of angle of inclination 30degrees. It is prevented from moving by a string parallel to the plane in which the force is F newton.
(Take g=10m/s^-2)

a) what is the weight force of the body?

b) is it possible to break the weight force into components.Calculate the size of the component:

(i) perpendicular to the plane:

(ii) Parallel to the plane:

c) What is the size or magnitude of the force F--->?

d) The string is released. With what acceleration does the mass move down the plane?

Answer 1

1) Force = 4N  ,  Mass = 0.5kg , Intial velocity(u) = 0 , Time = 5s

   Acceleration = force/mass = 4/0.5 = 8m/s^-2

   s = ut + (1/2)* a* (t^2)

     = (0)(5) + 1/2*(8)*(5)^2

     = 0 + 1/2 * (8) * (25) = 100m/s

2) 120N in support of motion  but 20N opposing motion,
     so the net force= 120-20 = 100N in support of motion,
     Acceleration = force/mass = 100/50 = 2m/s^-2
     v=5.5m/s , u=1m/s , a=2 m/s^2

      Speed(v) = u + at

                  5.5 = 1 + 2(t)

                  5.5-1 = 2t

                   t = 4.5/2 = 2.25sec

3a) Acceleration =force/mass = 20/5 = 4m/s^2,
   u= 100m/s , t=6sec , a = 4m/s^2

   Speed(v) = u + at =100 + 24 = 124m/s

b)The retardation is equal to acceleration in (a) in magnitude.
    retardation is a= - 4m/s^2 , u=100m/s  , t=6 sec
    Speed(v) = u + at = 100 + (-4)(6) = 100 - 24 = 76m/s

4a) Mass = 10kg , g=10m/s^-2

   Wieght = m*g = 10*10 = 100N

bi) Given that angle of inclination = 30degrees

     perpendicular to the plane = mg(cos30) = 100(0.866) = 86.6

ii)perpendicular to the plane = mg(sin30) = 100(0.5) = 50

c) Magnitude of the force(F)  = mg(sin30) = 100(0.5) = 50

d) Acceleration = force/mass = mg(sin30)/m = g(sin30) = 10(0.5) = 5m/s^-2