Four penguins are being pulled along very slippery (frictionless) ice by a curator. The masses of the three penguins are given below and so are two of the tensions. Find the penguin mass that is not given.
12kg---Unknown--111N--15kg---20kg--222N
After drawing the free-body force diagrams, I was lost.
Write the equations
F=ma
222=(20 + 15 + 12 + M)a
111= (12+M)a
so solve it, two unknowns, two equations. However, it is not that hard. There is another equation.
222-111 =(15+20)a so solve for A here, then solve for M from above.
1. Which of the following is not an example of an energy transfer?
1. A roller coaster being pulled to the top of the first hill
2. A roller coaster standing still allowing people to get on
3. A roller coaster falling down a hill
4. A roller coaster coming to a stop at the end of ride
thank you so much! I think I just overcomplicated the problem. thank you for making it much easier!
To solve this problem, we will use Newton's second law of motion, which states that the sum of the forces acting on an object is equal to the product of the object's mass and its acceleration.
Let's denote the masses of the penguins as follows:
m1 = 12 kg (given)
m2 = unknown
m3 = 15 kg (given)
m4 = 20 kg (given)
Now, let's analyze the forces acting on each penguin.
For penguin 1 (12 kg):
The only force acting on penguin 1 is the tension T1, which is given as 111 N.
For penguin 2 (unknown mass):
The forces acting on penguin 2 are the tension T1 (pulling towards the left) and the tension T2 (pulling towards the right). The net force acting on penguin 2 is zero since it is not accelerating. Therefore, we can write the equation:
T1 - T2 = 0
For penguin 3 (15 kg):
The forces acting on penguin 3 are the tension T2 and the weight (mg), where g represents the acceleration due to gravity. The weight is given by the equation W = mg, where m is the mass of the object and g is approximately 9.8 m/s^2.
For penguin 4 (20 kg):
The only force acting on penguin 4 is the tension T3, which is given as 222 N.
To solve the problem, we need information about the tension T2. Let's manipulate the equations to solve for T2.
From the equation T1 - T2 = 0, we can rewrite it as T2 = T1.
From the forces acting on penguin 3, we have T2 + mg = 0. Rearranging this equation, we get:
T2 = -mg.
Since we know that T2 = T1, we can write -mg = T1.
Now, we have the equation: -mg = 111 N.
We can now solve for the unknown mass, m2.
m2 = (-111 N) / (-9.8 m/s^2).
Calculating this, we find:
m2 ≈ 11.33 kg.
Therefore, the mass of penguin 2 is approximately 11.33 kg.