Question

A 2.50-kg stone is dropped from rest at a height of 3.75 m. What impulse does gravity impart to this stone from the instant it is dropped until it hits the ground

Answer 1

22.3Ns

Step-by-step explanation:

Hi!

To solve this exercise follow the steps below.

1. Find the weight of the stone by multiplying the gravity (9.8m / s ^ 2) by the mass.

W=mg

m=mass=2.5kg

g=gravity=9.8m / s ^ 2

W=(2.5)(9.8)=25.5N

2. Find the time it takes for the stone to touch the ground using the kinematic equation for constant acceleration.

Vf=Vo+a.t

y= VoT+\frac{1}{2}gt^{2}

Where

Vo = Initial speed =0

T = time

g=gravity=9.8m/s^2

Y= height= 3.75m

solving for time

`2y=gt^2\\t=\sqrt{ (2y)/(g) }=\sqrt{ (2(3.75))/(9.8) }=0.87s`

3. For a constant force such as weight, the impulse is calculated as the product between force and time.

I=wt

I=(25.5N)(0.87S)=22.3Ns