Question

A constant force of 3.2 N to the right acts on a 18.2 kg mass for 0.82 s. (a) Find the final velocity of the mass if it is initially at rest. m/s (b) Find the final velocity of the mass if it is initially moving along the x-axis with a velocity of 1.85 m/s to the left. m/s

Answer 1

Answer:

Explanation:

mass, m = 18.2 kg

time, t = 0.82 s

Force, F = 3.2 N right

initial velocity, u = 0 m/s

Let v is the final velocity.

(a) By the Newton's second law

F = ma

where a is the acceleration

3.2 = 18.2 x a

a = 0.176 m/s²

By using first equation of motion

v = u + at

v = 0 + 0.176 x 0.82

v = 0.144 m/s

(b) initial velocity, u = - 1.85 m/s

v = u + at

v = - 1.85 + 0.176 x 0.82

v = - 1.7 m/s

v = 1.7 m/s left

Answer 2

Explanation:

The given data is as follows.

      F = 3.2 N,      m = 18.2 kg,

      t = 0.82 sec

(a)  Formula for impulse is as follows.

          I = Ft = $\Delta P$

        Ft = $m(v_{f} - v_{i})$

or,    $v_{f} = \frac{Ft}{m} + v_{i}$

Putting the given values into the above formula as follows.

      $v_{f} = \frac{Ft}{m} + v_{i}$

              = $\frac{3.2 \times 0.82}{18.2} + 0$

              = 0.144 m/s

Therefore, final velocity of the mass if it is initially at rest is 0.144 m/s.

(b)  When velocity is 1.85 m/s to the left then, final velocity of the mass will be calculated as follows.

           Ft = $m(v_{f} - v_{i})$

or,      $v_{f} = \frac{Ft}{m} + v_{i}$

                  = $\frac{3.2 \times 0.82 sec}{18.2} - 1.85$

                  = -1.705 m/s

Hence, we can conclude that the final velocity of the mass if it is initially moving along the x-axis with a velocity of 1.85 m/s to the left is 1.705 m/s towards the left.