A mass of 3kg hangs at end of a string. Find the horizontal force needed to pull the mass sideways until the string is at 30 degree to the vertical
To solve this problem, we can break down the forces acting on the mass into vertical and horizontal components.
First, let's find the vertical component of the weight of the mass. The weight of an object is given by the formula:
Weight = mass × acceleration due to gravity
In this case, the mass is 3 kg and the acceleration due to gravity is 9.8 m/s².
Weight = 3 kg × 9.8 m/s² = 29.4 N
Therefore, the vertical component of the weight is 29.4 N.
Now, let's find the horizontal component of the tension in the string. The tension in the string can be divided into two components: one horizontal and one vertical.
Since the string is at a 30-degree angle to the vertical, the vertical component of the tension is given by:
Vertical Component of Tension = Tension × sin(30°)
The horizontal component of the tension is given by:
Horizontal Component of Tension = Tension × cos(30°)
We are looking for the horizontal force needed to pull the mass sideways, so we can set the horizontal component of the tension equal to the force we want to find. Let's call this force "F."
F = Tension × cos(30°)
We know that the vertical component of the tension is equal to the vertical component of the weight:
Vertical Component of Tension = 29.4 N
Therefore, we can solve for the tension in the string:
29.4 N = Tension × sin(30°)
Tension = 29.4 N / sin(30°)
Now, substitute the expression for the tension into the equation for the horizontal component of the tension:
F = (29.4 N / sin(30°)) × cos(30°)
F ≈ 52.9 N
The horizontal force needed to pull the mass sideways until the string is at a 30-degree angle to the vertical is approximately 52.9 N.