The pail and its contents have a mass of 60 kg. If the cable is 15 m long, determine the elevation of the pulley for equilibrium. Neglect the size of the pulley at A
Well, if we neglect the size of the pulley at A, it must feel pretty left out. I mean, who doesn't want to be noticed, right? But don't worry, little pulley at A, we'll give you some attention. Let's solve this!
To determine the elevation of the pulley for equilibrium, we need to consider the forces acting on it. We know that the pail and its contents have a mass of 60 kg, so we can find the weight of it by multiplying the mass by the acceleration due to gravity, which is approximately 9.8 m/s².
Weight of the pail = mass × acceleration due to gravity
Weight of the pail = 60 kg × 9.8 m/s²
Now, since the cable is 15 m long, the force acting to the right is equal to the force acting to the left. This means that the weight of the pail is equal to the tension in the cable on the left side.
Weight of the pail = Tension in the cable on the left side
We can use this information to find the elevation of the pulley. Let's solve for that, shall we?
Weight of the pail = Tension in the cable on the left side
60 kg × 9.8 m/s² = Tension in the cable on the left side
Tension in the cable on the left side = 588 N
Since the tension in the cable on the left side is equal to the weight of the pail, the elevation of the pulley for equilibrium would be zero. In other words, the pulley should be at the same height as the pail for everything to balance out.
So, there you have it! The clown bot has solved another puzzle for you. Now, go give that tiny pulley at A a hug!
To determine the elevation of the pulley for equilibrium, we need to consider the forces acting on the system.
First, let's define the forces acting on the pail:
1. Weight of the pail (Wp): The weight acts downward and can be calculated using the formula W = m * g, where m is the mass (60 kg) and g is the acceleration due to gravity (9.8 m/s^2).
Therefore, Wp = 60 kg * 9.8 m/s^2 = 588 N.
2. Tension in the cable (Tc): The tension in the cable acts upward and is the force required to balance the weight of the pail.
Next, let's consider the forces acting on the pulley:
1. Tension in the cable (Tp): The tension in the cable acts in both directions, but for equilibrium, it will be the same on both sides of the pulley.
To find the elevation of the pulley for equilibrium, we need to set up an equation that equates the sum of the forces acting upward to the sum of the forces acting downward. This can be expressed as:
ΣFup = ΣFdown
Considering the forces acting upward, it includes the tension in the cable for both sections of the cable:
ΣFup = Tc + Tp
Considering the forces acting downward, it includes the weight of the pail:
ΣFdown = Wp
Since we want the system to be in equilibrium, ΣFup should equal ΣFdown:
Tc + Tp = Wp
Now, let's substitute the known values and solve for Tp:
Tc + Tp = 588 N
Given that the cable is 15 m long, the tension at any point along the cable is constant. Therefore, the tension in the cable can be calculated using the formula:
Tc = Wp/2 = 588 N / 2 = 294 N
Substituting this back into the equation, we have:
294 N + Tp = 588 N
Solving for Tp:
Tp = 588 N - 294 N
Tp = 294 N
So, the tension in the cable at the pulley is 294 N.
Finally, to find the elevation of the pulley for equilibrium, we need to consider the length of the cable that supports the pail. Given that the cable is 15 m long, half of it is used for supporting the pail. Therefore, the elevation of the pulley will be:
Elevation = Length of cable - Half of the cable length
= 15 m - (15 m / 2)
= 15 m - 7.5 m
= 7.5 m
Hence, the elevation of the pulley for equilibrium is 7.5 m.
To determine the elevation of the pulley for equilibrium, we can use the principle of equilibrium, which states that the sum of the forces acting on an object should be equal to zero.
Let's break down the forces involved in this scenario:
1. Weight of the pail: The weight of the pail is the force acting downwards due to gravity. By using Newton's second law (F = m * g), where m is the mass of the pail and g is the acceleration due to gravity (approximately 9.8 m/s^2), we can calculate the weight of the pail.
Weight of the pail = mass * acceleration due to gravity
Weight of the pail = 60 kg * 9.8 m/s^2
2. Tension in the cable: The tension in the cable is the force acting upwards due to the resistance provided by the cable. This tension is equal throughout the cable. Let's call this tension T.
When the pail is in equilibrium, the tension force in the cable should be equal to the weight of the pail to balance it out. So, we can set up the equation:
Tension in the cable = Weight of the pail
Now, let's solve for the tension in the cable:
T = 60 kg * 9.8 m/s^2
Next, we can determine the elevation of the pulley.
Since the cable is 15 meters long and we neglect the size of the pulley at A, the elevation of the pulley is equal to the length of the cable. Therefore, the elevation of the pulley is 15 meters.