Question

A 10 kg object is attached to a spring and is pulled 0.5 m from its rest position at an angle of 30 degrees to the horizontal. The spring has a spring constant of k and is compressed 0.3 m. Calculate the potential energy stored in the spring and the rope, taking into account the horizontal and vertical components of the displacement.

Answer 1

Explanation:

The potentpotentialial energy stored in a spring is calculated by 1/2 * k * x^2, where k is the spring constant and x is the displacement from its rest position. The potential energy stored in the rope is calculated as m * g * h, where m is the object's mass, g is acceleration due to gravity and h is the object's vertical displacement. The total potential energy is the sum of these two energies. In this case, the horizontal and vertical components of the displacement can be calculated using trigonometry and then used to find the total potential energy stored in the spring and rope.

Answer 2

Explanation:

The potential energy stored in the spring can be calculated using the equation:

PE_spring = 1/2 * k * x^2

where k is the spring constant and x is the displacement of the spring from its rest position. In this case, x = 0.5 m.

The potential energy stored in the rope can be calculated as the gravitational potential energy of the object, which is given by:

PE_rope = m * g * h

where m is the mass of the object (10 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical displacement of the object.

The horizontal and vertical components of the displacement can be calculated using trigonometry:

x = 0.5 * cos(30) = 0.5 * sqrt(3)/2 m

y = 0.5 * sin(30) = 0.5/2 m

The total potential energy stored in the spring and rope is given by the sum of their individual potential energies:

PE = PE_spring + PE_rope = 1/2 * k * x^2 + m * g * h

Substituting in the given values, we find:

PE = 1/2 * k * (0.5 * sqrt(3)/2)^2 + 10 * 9.8 * (0.5/2 + 0.3)

Note: The spring constant (k) is not given, so the answer is given in terms of k.