The figure below shows an initially stationary block of mass m on a floor. A force of magnitude F = 0.550mg is then applied at upward angle = 19°.

(a) What is the magnitude of the acceleration of the block across the floor if the friction coefficients are μs = 0.595 and μk = 0.495?

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To find the magnitude of the acceleration of the block across the floor, we need to consider the forces acting on the block.

Let's break down the problem step by step:

Step 1: Identify the forces
The forces acting on the block are the gravitational force (mg), the normal force (N), and the force applied at an angle (F_applied). Additionally, there is a friction force (f) opposing the motion.

Step 2: Resolve the forces
Since the applied force (F_applied) is at an angle, we need to resolve it into its components parallel and perpendicular to the surface.

The component of the applied force parallel to the surface is F_parallel = F_applied * sin(θ), where θ is the angle of the applied force. In this case, θ = 19°.

The component of the applied force perpendicular to the surface is F_perpendicular = F_applied * cos(θ).

Step 3: Calculate the friction force
The friction force depends on whether the block is in the static or kinetic friction regime.

For static friction, the maximum friction force (f_max) can be calculated using the equation f_max = μs * N, where μs is the coefficient of static friction.

For kinetic friction, the friction force (f_kinetic) can be calculated using the equation f_kinetic = μk * N, where μk is the coefficient of kinetic friction. Once the block starts moving, the friction force will be kinetic.

The normal force (N) is equal to the weight of the block, which is N = mg.

Step 4: Determine if the block will be at rest or in motion
To determine whether the block will be at rest or in motion, we compare the maximum static friction force (f_max) to the component of the applied force parallel to the surface (F_parallel).

If F_parallel is smaller than f_max, the block will be at rest, and the friction force will be equal to the component of the applied force parallel to the surface (f = F_parallel).

If F_parallel is equal to or greater than f_max, the block will be in motion, and the friction force will be the kinetic friction force (f = f_kinetic).

Step 5: Calculate the net force and acceleration
The net force acting on the block is the sum of the forces in the horizontal direction.

If the block is at rest:
Net force = f = F_parallel
Acceleration (a) = Net force (f) / mass (m)

If the block is in motion:
Net force = f = f_kinetic
Acceleration (a) = Net force (f) / mass (m)

Let's calculate the acceleration for both cases.

Case 1: The block is at rest
f_max = μs * N
= μs * mg

Since F_parallel < f_max:
f = F_parallel
= F_applied * sin(θ)

Acceleration (a) = f / m
= F_applied * sin(θ) / m

Case 2: The block is in motion
f_kinetic = μk * N
= μk * mg

Since F_parallel >= f_kinetic:
f = f_kinetic
= μk * mg

Acceleration (a) = f / m
= μk * mg / m

Now, substitute the given values into the equations to find the magnitude of the acceleration of the block across the floor.

Two capacitors (c1 = 19 and c2 = 8 μF) are charged in series by a 14 V battery. Find the time constant of the charging circuit. (5 ohms)