When a pendulum is pulled back from its equilibrium position by 10∘, the restoring force is 1.0 N. When it is pulled back to 30∘

Answer:

0.0984

Explanation:

The first diagram below illustrates a free body diagram that will aid in resolving this problem.

According to the diagram, the force's horizontal component can be expressed as:

Substituting 42° for θ and 87.0° for

Meanwhile, the vertical component is:

Again substituting 42° for θ and 87.0° for

In resolving the vector, let A denote the components in mutually perpendicular directions.

The magnitudes of both components are illustrated in the second diagram provided and can be represented as A cos θ and A sin θ

The frictional force can be expressed as:

Where;

is the coefficient of friction

N = the normal force

Also, the normal reaction (N) is calculated as mg - F sin θ

Substituting . Normal reaction becomes:

By balancing the forces, the horizontal component of the force equals the frictional force.

The horizontal component is described as follows:

Rearranging the equation above to isolate leads to:

Substituting in the following values:

m = 73 kg

g = 9.8 m/s²

Thus:

Therefore, the coefficient of friction is = 0.0984

The electric flux through the cylindrical surface surrounding the infinite charged wire is given by the formula ∅E = E x 2πrl. To analyze this, we consider an infinitely long straight wire with a uniform linear charge density of λ Cm⁻¹. The electric field at a distance r from this charge can be evaluated using a cylindrical Gaussian surface of radius r and length l, oriented along the wire. Only the curved surface of the cylinder contributes to the total flux since the other surfaces are perpendicular to E.

The most effective question for the student to determine whether the substance is metal or nonmetal would be option C.

- The greatest potential energy increase occurs when the charge travels north. This happens because the charge is negative, which means it gains potential energy when moving in the same direction as the field (in contrast, a positive charge moving along the field loses potential energy, converting it to kinetic energy). The potential energy gained is calculated as the charge multiplied by the distance moved:


- The next largest increase occurs as the charge moves east. Here, the change in potential energy is actually zero since the charge moves perpendicular to the field, traversing points with constant potential. Therefore, there is no variation in potential energy in this case:


- Finally, when the charge moves south, it experiences a reduction in potential energy. This is due to moving against the electric field, and since it is a negative charge, it loses potential energy in this direction, which transforms into kinetic energy. Thus, in this scenario:

<span>Part b) Find your horizontal distance from the window (answer: 1.5 m)
Part c) Calculate the speed of the ball upon catching it (answer: 8.2 m/s)

I'm confused about what "42 degrees below the horizontal" means. Could someone provide guidance on how to approach this?</span>