Four balls are suspended by cords. The longer, top cord loops over a frictionless pulley and pulls with a force of magnitude 95 N on the wall to which it is attached. The tensions in the shorter cords are T1 = 56.0 N (between ball A & B), T2 = 46.7 N (between ball B & C), and T3 = 9.3 N (between ball C & D. What are the masses of each ball in kilograms?
Im not sure what type of equation to start off with this..
would acceleration = 0? .. since the tensions between a ball are in equilibrium?
If the cords are fixed to the wall, acceleraltion is zero.
Start with the tension at the wall, pulling toward the wall. It is supporting four balls.
95=A+B+C+D
Then, the next tension
T1= B+C+D and so on.
The acceleration of the balls is zero... They are fixed in space... They aren't falling are they?... They are suspended in air.
To start, start from the bottom up, it's a whole lot easier. First you would start out using newton's second law,
F=ma= T-M(of ball d)g(gravity constant)
0= T3-Mdg
-T= -Mdg
T=Mdg
T/g= Md
9.3/9.81=Md=.9480122324
That's the setup for finding the mass of ball d.
The setup for finding Ball c it
F=ma=0
F=T2-(Md+Mc)g
0=T2-(Md+Mc)g
-T2=-(Md+Mc)g
T2=(Md+Mc)g
T2/g = (Md+Mc)
So follow that approach and you should find the right answers hope it helps.
(t2/g)-Md =Mc
To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. Since the system is in equilibrium and not accelerating, the net force is zero.
Let's start by analyzing the tension at the wall. According to Newton's second law, the tension at the wall is equal to the sum of the tensions in the cords.
Tension at the wall = T1 + T2 + T3
Substituting the given values, we have:
95 N = 56.0 N + 46.7 N + 9.3 N
Now, we can solve for the tension between each pair of balls by using the equation:
T1 = T2 + T3
56.0 N = 46.7 N + 9.3 N
Lastly, we need to relate the tensions to the masses of the balls. The tension in each cord is equal to the weight of the ball it supports. The weight of an object can be calculated using the equation:
Weight = mass x acceleration due to gravity
In this case, the acceleration due to gravity is approximately 9.8 m/s^2.
Using these equations, we can solve for the masses of each ball:
For T1: 56.0 N = mass of ball B + mass of ball C + mass of ball D
For T2: 46.7 N = mass of ball C + mass of ball D
For T3: 9.3 N = mass of ball D
Now we have a system of three equations with three unknowns. Solving these equations simultaneously will give us the masses of each ball.