(a) To find the magnitude of the push (force), we need to consider the forces acting on the sphere in the horizontal direction. The only horizontal force is the push from the breeze, which we'll call F. Since the sphere is in equilibrium (not accelerating), the sum of the forces in the horizontal direction must be zero. This means that the horizontal component of the tension in the cord must balance the push from the breeze.

The horizontal component of the tension (T) can be found using the equation Tsin(θ) = F, where θ is the angle the cord makes with the vertical. Rearranging for F gives F = Tsin(θ).

We don't know T yet, but we can find it by considering the forces in the vertical direction. The only vertical forces are the weight of the sphere (mg, where m is the mass and g is the acceleration due to gravity) and the vertical component of the tension (Tcos(θ)). Since the sphere is in equilibrium, these forces must balance, so mg = Tcos(θ). Rearranging for T gives T = mg/cos(θ).

Substituting this into the equation for F gives F = (mg/cos(θ))sin(θ) = mgtan(θ). Substituting the given values (m = 3.4 ✕ 10^-4 kg, g = 9.8 m/s^2, θ = 41°) gives F = (3.4 ✕ 10^-4 kg)(9.8 m/s^2)tan(41°) = 0.0027 N.

(b) The tension in the cord can be found using the equation T = mg/cos(θ). Substituting the given values gives T = (3.4 ✕ 10^-4 kg)(9.8 m/s^2)/cos(41°) = 0.0034 N.

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(a) To find the magnitude of the push (force), we need to consider the forces acting on the sphere in the horizontal direction. The only horizontal force is the push from the breeze, which we'll call F. Since the sphere is in equilibrium (not accelerating), the sum of the forces in the horizontal direction must be zero. This means that the horizontal component of the tension in the cord must balance the push from the breeze.

The horizontal component of the tension (T) can be found using the equation Tsin(θ) = F, where θ is the angle the cord makes with the vertical. Rearranging for F gives F = Tsin(θ).

We don't know T yet, but we can find it by considering the forces in the vertical direction. The only vertical forces are the weight of the sphere (mg, where m is the mass and g is the acceleration due to gravity) and the vertical component of the tension (Tcos(θ)). Since the sphere is in equilibrium, these forces must balance, so mg = Tcos(θ). Rearranging for T gives T = mg/cos(θ).

Substituting this into the equation for F gives F = (mg/cos(θ))sin(θ) = mgtan(θ). Substituting the given values (m = 3.4 ✕ 10^-4 kg, g = 9.8 m/s^2, θ = 41°) gives F = (3.4 ✕ 10^-4 kg)(9.8 m/s^2)tan(41°) = 0.0027 N.

(b) The tension in the cord can be found using the equation T = mg/cos(θ). Substituting the given values gives T = (3.4 ✕ 10^-4 kg)(9.8 m/s^2)/cos(41°) = 0.0034 N.

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(a) To find the magnitude of the push (force), we need to consider the forces acting on the sphere in the horizontal direction. The only horizontal force is the push from the breeze, which we'll call F. Since the sphere is in equilibrium (not accelerating), the sum of the forces in the horizontal direction must be zero. This means that the horizontal component of the tension in the cord must balance the push from the breeze.

The horizontal component of the tension (T) can be found using the equation Tsin(θ) = F, where θ is the angle the cord makes with the vertical. Rearranging for F gives F = Tsin(θ).

We don't know T yet, but we can find it by considering the forces in the vertical direction. The only vertical forces are the weight of the sphere (mg, where m is the mass and g is the acceleration due to gravity) and the vertical component of the tension (Tcos(θ)). Since the sphere is in equilibrium, these forces must balance, so mg = Tcos(θ). Rearranging for T gives T = mg/cos(θ).

Substituting this into the equation for F gives F = (mg/cos(θ))sin(θ) = mgtan(θ). Substituting the given values (m = 3.4 ✕ 10^-4 kg, g = 9.8 m/s^2, θ = 41°) gives F = (3.4 ✕ 10^-4 kg)(9.8 m/s^2)tan(41°) = 0.0027 N.

(b) The tension in the cord can be found using the equation T = mg/cos(θ). Substituting the given values gives T = (3.4 ✕ 10^-4 kg)(9.8 m/s^2)/cos(41°) = 0.0034 N.

A sphere of mass 3.4 ✕ 10-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes a constant angle of 41° with the vertical.(a) Find the magnitude of that push. N(b) Find the tension in the cord. N

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