A man enters an elevator holding two boxes-one on top of the other. The top has a mass of 6.0 kg and the buttom box has a mass of 8.0 kg. The man sets the two boxes on a metric scale registers a value of 166N; this is the upward force upon the bottom box. Determine the acceleration of the elevator (and boxes) and determine the forces acting between the boxes.
Ps. I need solutin thank you so much....
(Mt+Mb)g+(Mt+Ma)a)=166
solve for a.
now, the aforce between the two boxes:
Mt(g+a) is that force.
thank you so much
acceleration is 11m/s
what is the meaning of Mt,Mb,and Ma?
What is the solution of that?
To determine the acceleration of the elevator and the forces acting between the boxes, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
Let's assume the acceleration of the elevator and boxes is denoted as "a".
First, determine the total mass of the two boxes by adding their individual masses:
Mass of top box (m1) = 6.0 kg
Mass of bottom box (m2) = 8.0 kg
Total mass (m) = m1 + m2 = 6.0 kg + 8.0 kg = 14.0 kg
Now, let's write down the forces acting on each box:
For the top box:
- Force due to its weight (mg1) = mass (m1) × acceleration due to gravity (g = 9.8 m/s^2)
For the bottom box:
- Force due to its weight (mg2) = mass (m2) × acceleration due to gravity (g = 9.8 m/s^2)
- Force acting upward (F) = 166 N
According to Newton's second law, the net force acting on each box is equal to the mass of the box multiplied by its acceleration:
For the top box:
mg1 = m1 × a
For the bottom box:
mg2 + F = m2 × a
Now, let's substitute in the values we have:
m1 × a = 6.0 kg × 9.8 m/s^2
m2 × a + 166 N = 8.0 kg × 9.8 m/s^2
Simplifying these equations, we get:
6.0a = 58.8
8.0a + 166 = 78.4
Solving these equations simultaneously, we find:
a = 9.8 m/s^2
Therefore, the acceleration of the elevator (and boxes) is 9.8 m/s^2.
To determine the forces acting between the boxes, we can substitute the value of "a" back into one of the equations:
m1 × a = 6.0 kg × 9.8 m/s^2
Solving this equation, we find:
Force acting between the boxes = m1 × a = 6.0 kg × 9.8 m/s^2 = 58.8 N
Thus, the force acting between the boxes is 58.8 N.