In the figure below, a uniform sphere of mass m = 2.50 kg and radius r = 2.4 cm is held in place by a massless rope attached to a frictionless wall a distance L = 10.2 cm above the center of the sphere.

Question

In the figure below, a uniform sphere of mass m = 2.50 kg and radius r = 2.4 cm is held in place by a massless rope attached to a frictionless wall a distance L = 10.2 cm above the center of the sphere.

(a) What is the tension in the rope?
N

(b) What is the force on the sphere from the wall?
N

Answer 1

I don't understand the figure.

Answer 2

To find the tension in the rope, we need to consider the equilibrium condition in the vertical direction.

(a) The tension in the rope can be found by balancing the weight of the sphere with the vertical component of the tension.

Step 1: Calculate the weight of the sphere.
The weight of the sphere can be calculated using the formula: weight = mass * acceleration due to gravity.

mass of the sphere, m = 2.50 kg
acceleration due to gravity, g = 9.8 m/s^2

weight = m * g = 2.50 kg * 9.8 m/s^2

Step 2: Calculate the vertical component of the tension.
The vertical component of tension balances the weight of the sphere, so it must be equal to the weight of the sphere.

vertical component of tension = weight of the sphere = m * g

So, the tension in the rope is equal to the vertical component of the tension.

Tension = vertical component of tension = m * g

Substituting the given values:

Tension = 2.50 kg * 9.8 m/s^2

Calculate the value of the tension to find the answer in Newtons.

(b) The force on the sphere from the wall can be found by considering the horizontal equilibrium.

Step 1: Determine the horizontal component of the tension.
Since the sphere is at rest, the net force in the horizontal direction must be zero. Therefore, the horizontal component of the tension is balanced by the force from the wall.

horizontal component of tension = force from the wall

Step 2: Determine the value of the horizontal component of the tension.
The force from the wall can be determined using the formula: force from the wall = horizontal component of tension.

So, the force from the wall is equal to the horizontal component of the tension.

Force from wall = horizontal component of tension

Substituting the given values, use the previously calculated tension:

Force from wall = Tension

Calculate the value of the force from the wall to find the answer in Newtons.