How Is the Center of Gravity Calculated on a Plank?

[neoljeol]

hey all, I am having prob with two questions,

the first one goes like this.

"two scales are separated by 2.00 m, and a plank of mass 4.00 kg is placed between them. each scale is observed to read 2.00 kg. a person now lies on the plank, after which the right scale reads 30.0 kg and the left scale reads 50.0 kg. how far from the right scale is the person's center of gravity located?"

the answer is either 1.25m, or 1.26m, depending on if you ommited the mass of the table or not. I didn't and got 1.26m

and a kinematics question i need help with

A 25 N force acts on a 3.5 kg mass acceleration it in a location where the friction between the cart and the surface is 4.8 N. What is the velocity of the cart after it has traveled 12.6 m?

i got 12.1 but not sure if its correct

any help would be appreciated

thanks =D

edit my work:

for the first problwm

sum y = 0
(50g + 30g) - (f person + 4g) = -
f person = 744.8N

sum t = 0
rf + rf - rf = 0
(744.8n)(x) + (4g)(1m) - (2m)(50g) = 0
x = 1.26m

second problem:

a = 5.7 m/s^2
d = .5at^2
t = 2.1 s
v = at
v = 11.9 m/s

 

[Jhero]

Hi there,

I'm happy to help with your questions. For the first problem, you are correct that the answer would be 1.26m. It's important to include the mass of the plank when calculating the center of gravity.

For the second problem, you are on the right track. However, I think there may be a small mistake in your calculations. The correct answer should be 13.1 m/s. Here's how I got that answer:

Firstly, we need to find the net force acting on the cart:

Fnet = ma
Fnet = (25 N - 4.8 N) = 20.2 N

Next, we can use the equation v^2 = u^2 + 2as to find the final velocity:

v^2 = u^2 + 2as
v^2 = 0 + 2(20.2 N)(12.6 m)
v^2 = 510.48
v = √510.48
v = 22.6 m/s

However, this is the final velocity of the cart. To find the average velocity, we need to divide this by 2:

vavg = v/2
vavg = 22.6 m/s / 2
vavg = 11.3 m/s

So the final answer would be 11.3 m/s, or 13.1 m/s depending on whether you want the final or average velocity.

I hope this helps! Let me know if you have any other questions or need further clarification. Good luck!