Question

A force in the negative direction of an x axis is applied for 34 ms to a 0.40 kg ball initially moving at 16 m/s in the positive direction of the axis. The force varies in magnitude, and the impulse has magnitude 32.4 N·s.

(a) What is the ball's speed just after the force is applied?
____m/s
(b) What is the average magnitude of the force?
___N

Answer 1

Impulse = Change in momentum of the body
Since here mass is a constant property momentum depends only on the velocity-
Initial momentum = 16 x 0.4 = 6.4 N.s
Final momentum = 6.4 - 32.4 = -26 N.s
Final velocity = -26/0.4 = -65 m/s which means 65 m/s in the negative x direction (Answer)

Since the change in velocity = 16- (-65) = 81 m/s and it takes 34 ms to change thus
average acceleration = 81/0.034 = 2382.35 m/s^2
Average Force = mass x acceleration = 0.4 * 2382.35 = 952.9 N (Answer)

Answer 2

(a) impulse = F x t = m x a x t

     therefore: -32.4 = 0.4* (a) * t (minus since it is in the negative direction)

                     -32.4 = 0.4 (a) * 0.034

                     -32.4 = 0.0136a

                     a = -2382.4 m/s²

    and Using kinemtaic equations : v = v₀ + at

          v = 16 - 2382.4(0.034)

          v = -65 m/s The minus represent its direction,(in the negative direction )

(b) Avg Force = impulse/ time = 32.4 / 0.034 = 952.95 N

Answer 3

a) ball speed 0.4(v-16) = 32.4
v = 97 m/s
b) F = 32.4/34*10^-3 =952.94 N