Answer:
(a) 64.6 kg/ms
(b) 4088.61 N
Explanation:
(a)
I = mΔv.................. Equation 1
Where I = impulse acting on the ball, Δv = change in velocity.
But,
Δv = v-u.............. Equation 2
Where v = final velocity, u = initial velocity.
Substitute equation 2 into equation 1
I = m(v-u).................. Equation 3
Assuming: upwards to be positive
Given: m = 1.9 kg, v = 9 m/s, u = -25 m/s (downward)
Substitute into equation 3
I = 1.9[9-(25)]
I = 1.9(9+25)
I = 1.9(34)
I = 64.6 kgm/s.
(b)
F = I/t................... Equation 4
Where F = Average force on the floor from the ball, t = time of contact of the floor with the ball.
Given: I = 64.6 kgm/s, t = 0.0158 s
Substitute into equation 4
F = 64.6/0.0158
F = 4088.61 N
Answer:
A) Impulse = 64.6 N.s
B) Force = 4088.6 N
Explanation:
We are given;
Mass of ball;m = 1.9 kg
Initial velocity of ball;u = -25 m/s (negative value because ball was drop downward)
Final velocity of ball;v = 9 m/s
From Newton's second law of motion, we know that;
Impulse = Change in momentum
Thus;
Impulse = final momentum - initial momentum = mv - mu
Thus;
Impulse = m(v - u)
Plugging in the relevant values, we have;
Impulse = 1.9(9 - (-25)
Impulse = 1.9(9 + 25)
Impulse = 1.9(34)
Impulse = 64.6 N.s
B) As said earlier,
impulse = 64.6 N.s
Now, we are looking for the magnitude of the average force.
Now, Impulse is also expressed as Force x time.
Thus,
Force x time = 64.6 N.s
We are given time as 0.0158 s
Thus, making Force the subject of the formula, we now have;
Force = 64.6/0.0158
Force = 4088.6 N
