A force of 40.0 N accelerates a 5.0-kg block at 6.0m/s^2 along a horizontal surface. How large is the ....?

Question

A force of 40.0 N accelerates a 5.0-kg block at 6.0m/s^2 along a horizontal surface.

a. how large is the frictional force?
b. what is the coefficient of friction?

Please help me with these questions.
I'm having trouble understanding them.

Answer 1

40N on a frictionless surface would accelerate 5 kg at 8 m/s² (F = ma) so there must be a total of only 6.666N acting on the ice. That means that a frictional force of 3.333N is acting in the opposite direction. Since the coefficient of kinetic friction is calculated as the frictional force divided by the normal force, it must be
Fk = 3.333/5*9.8 = 3.333/49 = .068


Doug

Answer 2

An external force equal to 40 N is applied to the block in a horizontal direction. Once the block has overcome the initial static friction opposing its motion (greater than the dynamic friction it experiences during motion) it moves in a horizontal direction. It experiences a constant frictional force B which opposes it motion. Thus the net force, F, acting on the block in the direction of its motion is given by:

F = 40 - B (equation 1)

We know from Newton's second law of motion that a mass, m, experiences an acceleration, a, when acted on by a force, F, given by the equation:

F = m * a

Substituting this into equation 1:

m * a = 40 - B

The block in question has a mass of 5 kg and experiences an acceleration of 6 m/s^2. Thus:

5 * 6 = 40 - B

Simplifying the left hand side of this equation:

30 = 40 - B

Rearranging this equation:

B = 40 - 30 = 10

Thus, the frictional force experienced by the block is 10 N.

We know from Newton's third law that if body X applies a force to body Y, then body Y applies an equal and opposite force to body X. The block obviously has a weight. It therefore applies a vertical and downward force to the surface on which it sits. Newton's thrid law then tells us that the surface must thus apply a vertical and upward force on the block. Let R be the force of the surface on the block.

It is observed that the frictional force experienced by a body in motion is proportional to the vertical upward force it feels from the surface beneath. The constant of proportionality, u, is referred to as the "coeffcient of friction". Thus:

B = u * R

Rearranging this equation:

u = B / R (equation 2)

The block obviously doesn't move in a vertical direction. Thus the net force in this direction must be equal to zero. As well as the force the block experiences due to its contact with the surface below, it feels a gravitational force in the opposite direction. This is its weight, W. For the block to experience no net force in the vertical direction, the contact force must be equal to the weight of the block. Thus:

R = W (equation 3)

If g is the "acceleration due to gravity", the weight, W, of a mass, m, is given by the equation:

W = m * g

Substituting this into equation 3:

R = m * g

On the Earth's surface, g = 10 m/s^2 (approximately). Thus, for the block in quesion:

R = 5 * 10 = 50

Substituting this result into equation 2:

u = B / 50

But remember that B = 10. Thus:

u = 10 / 50 = 0.2

In other words, the "coefficient of friction" is 0.2.

Answer 3

Without friction, a 5 kg block accelerated at 6 m/s2 would require a force of 30 N:

F = Ma = 5kg x 6 m/s2 = 30 N

Since the actual force is 40 N, we must assume that the force of friction is the difference between the two, or 10 N

Recall that the friction force, F = uM, where u = coefficient of friction.

Therefore, u = F/M or

u = 10 N / 5 kg = 2 m/s2

Answer 4

because of the fact tension internet= mass x acceleration, tension utilized plus tension friction = mass x accel......... Fa+Ff=ma plug in what all of us understand, 40 + Ff = (5)(6) resolve for Ff this is -10, so friction is 10 newtons opposite the direction of action. Coefficcient of friction is got here upon via dividing the traditional tension into the stress of friciton. Coefficient is represented via mu sub ok (for kinetic friction), so uk = Ff/Fn uk = 10/40 9 uk=.204

Answer 5

Calculate from these equations.
F - fr = m*a, where F = net force 40 N, fr, friction, m= mass, a=acceleration.
then fr = F - m*a,
fr = u*m*g; so u=fr/(m*g)
g acceleration of gravity.
Now put the figures and calculate with your calculator.