A ball weighing 50N is pulled back by a rope to an angle of 20 degrees (the rope that the ball hangs from). Find the tension in the pulling rope.

The tension in the pulling rope can be calculated using the equation T = mgsinθ, where m is the mass of the ball, g is the acceleration due to gravity, and θ is the angle of the rope.

T = (50N)(9.8m/s2)(sin20°)

T = 49.1N

To find the tension in the pulling rope, we need to consider the forces acting on the ball. Let's analyze the situation step-by-step:

Step 1: Draw a force diagram.
- There are two forces acting on the ball: the weight of the ball (50N) acting vertically downward and the tension in the rope acting at an angle of 20 degrees.

Step 2: Resolve the forces into their components.
- The weight can be resolved into two components: one parallel to the rope (acting in the opposite direction) and one perpendicular to the rope.
- The component parallel to the rope is given by: W_parallel = Weight * sin(theta)
- The component perpendicular to the rope is given by: W_perpendicular = Weight * cos(theta), where theta is the angle between the rope and the vertical direction.

Step 3: Calculate the tension in the rope.
- Since the ball is in equilibrium, the tension in the rope must be equal in magnitude but opposite in direction to the parallel component of the weight. Therefore, the tension in the rope is: Tension = W_parallel = Weight * sin(theta).

Now let's substitute the given values into the equations:

Weight = 50N (Given)
theta = 20 degrees (Given)

Calculating the tension in the rope:

Tension = Weight * sin(theta)
Tension = 50N * sin(20)
Tension ≈ 17.17 N (rounded to two decimal places)

Therefore, the tension in the pulling rope is approximately 17.17 N.

To find the tension in the pulling rope, we can break down the forces acting on the ball.

In this case, we have two forces acting on the ball:
1. The gravitational force acting vertically downwards, which is equal to the weight of the ball.
2. The tension in the pulling rope, acting in the direction of the rope.

To solve for the tension, we need to resolve the weight of the ball into two components: one parallel to the direction of the rope and one perpendicular to it.

Let's start by finding the component of the weight parallel to the rope:

Weight of the ball = 50 N
Angle between the weight and the rope = 20 degrees

The component of the weight parallel to the rope is given by:
Parallel component = weight * sin(angle)
= 50 * sin(20)
≈ 17.17 N

Now, since the ball is in equilibrium, the tension in the pulling rope must be equal to the parallel component of the weight. Therefore, the tension in the rope is approximately 17.17 N.