A 5.70 kg block located on a horizontal floor is pulled by a cord that exerts a force F = 10.4 N at an angle theta = 27.5° above the horizontal. The coefficient of kinetic friction between the block and the floor is 0.10. What is the speed of the block 6.1 s after it starts moving?

I don't know how to do these equations in which they want you to find speed. A little help would be much appreciated.

This is a lot like your previous problem.

There is a force 10.4 cos 27.5 or 9.22 N horizontal from the cord.

There is a force 10.4 sin 27.5 or 4.80 N up from the cord

The force the block exerts down on the floor is the weight - the pull up from the cord
m g - 4.80 N
= 5.70(9.8) - 4.8 = 51.06 N normal to floor

So the friction force = .1 (51.06) = 5.11 N friction force
the net horizontal force on the block is therefore
9.22 - 5.11 = 4.11 N
now do F = m a
4.11 = 5.70 a
a = .721 m/s^2
initial speed o is 0 we assume
v = 0 + a t = .721 (6.1)= 4.4 m/s

Ohh ok great I understand.

Thanks a lot. :)

To find the speed of the block 6.1 seconds after it starts moving, we can break down the problem into different steps:

Step 1: Calculate the net force acting on the block.
The net force is the vector sum of all the forces acting on the block. In this case, the forces acting on the block are the applied force F and the force of friction.

- The applied force F can be broken down into its horizontal and vertical components using trigonometry. The horizontal component, Fx, is given by F * cos(theta), and the vertical component, Fy, is given by F * sin(theta).
Fx = 10.4 N * cos(27.5°)
Fy = 10.4 N * sin(27.5°)

- The force of friction is given by the coefficient of kinetic friction (μk) multiplied by the normal force (N) experienced by the block. The normal force is equal to the weight of the block, which is mg, where m is the mass of the block and g is the acceleration due to gravity.
N = mg = 5.70 kg * 9.8 m/s^2
Force of friction (Ff) = μk * N = 0.10 * (5.70 kg * 9.8 m/s^2)

- The net force in the horizontal direction is equal to the applied force in the horizontal direction minus the force of friction.
Net force (Fnet_x) = Fx - Ff

Step 2: Calculate the acceleration of the block.
The net force acting on an object is related to its mass and acceleration by Newton's second law, F = ma. In this case, since we are interested in the horizontal motion of the block, we can use Fnet_x as the net force and divide it by the mass (m) to find the acceleration (a).
Fnet_x = m * a
a = Fnet_x / m

Step 3: Calculate the final velocity of the block.
The final velocity (vf) of an object after a certain time (t) can be found using the equation vf = vi + at, where vi is the initial velocity (which is 0 in this case since the block starts from rest).

- First, calculate the initial velocity (vi) using the formula for the horizontal component of the applied force:
vi = (Fx - Ff) * t / m

- Then, calculate the final velocity (vf) using the above equation:
vf = vi + a * t

Step 4: Substitute the known values into the equations and calculate the final velocity.
Substitute the values of Fx, Ff, m, and t into the equations derived in the previous steps and calculate vf.

Please note that I have provided the general steps to solve the problem. You can substitute the numerical values given in the question to solve the equations and find the speed of the block 6.1 seconds after it starts moving.