A 15kg mass suspended from a ceiling is pulled aside with a horizontal force,F,as shown. Calculate the value of the tension, T. (g= 10m/s²)
In this situation, the tension force and the gravitational force are the only vertical forces acting on the mass. Since the mass is not accelerating vertically, the tension force and the gravitational force must be equal in magnitude.
First, we need to find the gravitational force acting on the mass. The gravitational force can be calculated using the equation:
Fg = mg
Where:
Fg = gravitational force
m = mass
g = acceleration due to gravity
Given:
m = 15 kg
g = 10 m/s²
Fg = 15 kg * 10 m/s²
Fg = 150 N
Next, we can use this value to find the tension force:
T = Fg
T = 150 N
Therefore, the tension force, T, is equal to 150 N.
To determine the value of the tension, T, we need to consider the forces acting on the mass.
Step 1: Draw a free body diagram of the mass, showing all the forces acting on it.
In this case, we have the weight force acting vertically downward and the tension force acting horizontally to the right.
```
----------[Tension, T]
|
|
[Weight, Fg = mg]
```
Step 2: Identify the forces and their directions.
The weight force, Fg, acts vertically downward, and the tension force, T, acts horizontally to the right.
Step 3: Apply Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration.
```
Net force = mass × acceleration
```
Since the mass is not accelerating vertically (it remains stationary in the vertical direction), the net force in the vertical direction is zero.
Thus, the weight force must be balanced by an equal and opposite force, which is the tension force acting vertically upward.
Step 4: Set up the equation for the vertical forces:
```
T - Fg = 0
```
The weight force is given by Fg = mg, where m is the mass of the object and g is the acceleration due to gravity.
Step 5: Substitute the values into the equation and solve for T.
```
T - mg = 0
T = mg
```
Given that the mass, m, is 15 kg and the acceleration due to gravity, g, is 10 m/s², we can substitute these values into the equation:
```
T = 15 kg × 10 m/s²
T = 150 N
```
Therefore, the value of the tension, T, is 150 N.