a block is pushed up
against the wall. Let the mass of the block be
m = 2.8 kg, the coefficient of kinetic friction
between the block and the wall be µ = 0.56,
and θ = 61◦
. Suppose F = 73 N.
The acceleration of gravity is 9.8 m/s
2
Find the force of friction.
Answer in units of N
Well, well, well, it looks like we have a block that's stuck between a rock and a hard place, or should I say, a block and a wall. Let's figure out the force of friction that's giving this block a hard time.
First things first, we need to find the component of the force pushing the block against the wall. This force perpendicular to the wall can be found by taking the force of gravity (mg) and multiplying it by the sine of the angle (theta).
So, F_perpendicular = mg * sin(theta)
= 2.8 kg * 9.8 m/s^2 * sin(61)
= 47.4985 N
Now, let's calculate the force of friction by multiplying the coefficient of kinetic friction (mu) with the force perpendicular.
Force of friction = mu * F_perpendicular
= 0.56 * 47.4985 N
= 26.5996 N
Ah, just like that, we found the force of friction. It's a slippery 26.5996 N.
To find the force of friction, we can use the equation:
Force of friction (F_friction) = µ * Normal force
The normal force can be calculated by finding the component of gravity acting perpendicular to the wall. The formula for the normal force is:
Normal force (N) = m * g * cos(θ)
First, let's calculate the normal force:
m = 2.8 kg (mass of the block)
g = 9.8 m/s^2 (acceleration due to gravity)
θ = 61°
Normal force (N) = 2.8 kg * 9.8 m/s^2 * cos(61°)
Now, let's calculate the force of friction using the given coefficient of kinetic friction:
µ = 0.56 (coefficient of kinetic friction)
Force of friction (F_friction) = 0.56 * N
Plug in the value of N and calculate:
Force of friction (F_friction) = 0.56 * (2.8 kg * 9.8 m/s^2 * cos(61°))
Solve the expression to find the force of friction, rounding the answer to the appropriate number of significant digits.
To find the force of friction, we can use the formula:
force of friction = coefficient of friction * normal force
In this case, the normal force is the component of the weight of the block perpendicular to the wall. Since the block is pushed up against the wall, the normal force is equal to the weight of the block (mg) times the cosine of the angle between the weight vector and the wall (θ).
normal force = mg * cos(θ)
Substituting the given values:
m = 2.8 kg
g = 9.8 m/s^2
θ = 61°
normal force = (2.8 kg * 9.8 m/s^2) * cos(61°)
Now, let's calculate the normal force:
normal force = (2.8 * 9.8) * cos(61°)
normal force = 27.44 * cos(61°)
normal force ≈ 13.72 N
Next, we can calculate the force of friction:
force of friction = coefficient of friction * normal force
Given:
µ = 0.56
normal force = 13.72 N
force of friction = 0.56 * 13.72
force of friction ≈ 7.67 N
Therefore, the force of friction is approximately 7.67 N.