A block of mass m is pushed along a horizontal table by a force F= 70 N a an angle 55 degrees with the horizontal. The coefficient of kinetic friction is 0.3

Write Newtons second law using vectors. Write newtons second law using x scalar components

To write Newton's second law using vectors, we need to consider the net force acting on the block and its acceleration. Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

In vector form, Newton's second law can be written as:

Fnet = m * a

Where:
- Fnet represents the net force acting on the object,
- m is the mass of the object, and
- a is the acceleration of the object.

In this case, we have a force (F) acting on the block at an angle of 55 degrees with the horizontal. To find the net force, we need to resolve the force into its horizontal and vertical components.

The horizontal component of the force can be calculated using:

Fhorizontal = F * cos(θ)

Where:
- Fhorizontal represents the force component acting horizontally (parallel to the table),
- F is the magnitude of the force (70 N in this case),
- θ is the angle between the force and the horizontal (55 degrees).

Substituting the given values, we have:

Fhorizontal = 70 N * cos(55°)

Next, let's calculate the vertical component of the force using:

Fvertical = F * sin(θ)

Where:
- Fvertical represents the force component acting vertically (perpendicular to the table).

Substituting the values:

Fvertical = 70 N * sin(55°)

Now, we can find the net force by subtracting the force of friction from the horizontal component of the force:

Fnet = Fhorizontal - Friction

The force of friction can be calculated using the equation:

Friction = μ * N

Where:
- Friction represents the force of friction,
- μ is the coefficient of kinetic friction (given as 0.3),
- N is the normal force.

Since the block is on a horizontal table, the normal force (N) acting on the block is equal to its weight (mg), where g is the acceleration due to gravity (9.8 m/s^2).

Thus,

Friction = 0.3 * (mg)

Finally, substituting the values back into the equation for Fnet, we have:

Fnet = Fhorizontal - 0.3 * (mg)

To write Newton's second law using scalar components, we can use the same principles but express the forces and acceleration in terms of their x-direction scalar components.

In the x-direction, the only force acting on the block is the horizontal component of the force:

Fnet,x = Fhorizontal - Friction

Since there is no acceleration in the vertical direction, Fnet,y is equal to zero:

Fnet,y = 0

Therefore, the complete expression of Newton's second law using x scalar components is:

Fnet = (Fnet,x)i + (Fnet,y)j

Where i and j are unit vectors along the x and y directions, respectively.