Question

A 4.9 kg object hangs at one end of a rope that is attached to a support on a railroad boxcar. When the car accelerates to the right, the rope makes an angle of 25 degrees with the vertical. What is the tension in the rope?

Answer 1

To determine the tension in the rope, separate the weight of the object and the horizontal force into components. Then, use the angle to calculate the vertical component of tension and solve for the total tension using T = mg / cos(25°), taking gravity and the mass into account.

Step-by-step explanation:

To determine the tension in the rope when a 4.9 kg object hangs on it from a railroad boxcar that is accelerating, we must consider the forces acting on the object. The object experiences a downward gravitational force (its weight) and a horizontal force due to the acceleration of the boxcar. To find the tension, we draw a free-body diagram and apply Newton's second law of motion.

First, we'll separate the forces into their components:

• The weight of the object, which is straight down: W = mg = 4.9 kg * 9.81 m/s²
• The tension in the rope has two components due to the angle: the vertical component (T_v) which opposes gravity, and the horizontal component (T_h) which is due to the boxcar's acceleration.

Using the angle given, 25 degrees, we can write:

• T_v = T * cos(25°)
• T_h = T * sin(25°)

Since the object is not moving vertically, T_v equals the weight of the object:

T * cos(25°) = mg

Which we can solve for T:

T = mg / cos(25°)

Plugging in the numbers gives us:

T = (4.9 kg * 9.81 m/s²) / cos(25°)

After calculating, we find the tension in the rope.