A 3.20 kg block is pushed along the ceiling with a constant applied force of 85.0 N that acts at an angle of 55.0° with the horizontal.
The block accelerates to the right at 7.50 m/s2.
Determine the coefficient of kinetic friction between block and ceiling.
Would appreciate some guidance on how the Normal force works in this case
Ah, the coefficient of kinetic friction strikes again! Alright, let's break this down with some Clown-friendly guidance on the normal force.
In this case, the normal force refers to the force exerted by the ceiling on the block, which counteracts the force of gravity pulling the block downward. The normal force is always perpendicular to the surface of contact.
Now, since the block is pushed against the ceiling, there are two main forces at play: the applied force and the force of friction. The applied force is the one given in the problem (85.0 N at an angle of 55.0° with the horizontal), and the force of friction is the one we're after.
To find the normal force, we first need to resolve the applied force into its horizontal and vertical components. Using some trigonometry, we can find that the vertical component of the applied force is 85.0 N * sin(55.0°), and this will be equal to the normal force.
Since the block is accelerating to the right, we can conclude that the applied force is greater than the force of kinetic friction. So, the force of kinetic friction can be determined as the mass of the block multiplied by the acceleration (F = ma).
The tricky part is that the frictional force and the normal force are related by the coefficient of kinetic friction. We can express the force of kinetic friction as the product of the coefficient of kinetic friction and the normal force.
Considering all this, we can set up the following equation:
85.0 N * sin(55.0°) = (3.20 kg) * (7.50 m/s^2) + (coefficient of kinetic friction) * (85.0 N * cos(55.0°))
From here, you can solve for the coefficient of kinetic friction. I hope this explanation brings a smile to your face as you tackle this problem!
To determine the coefficient of kinetic friction between the block and the ceiling, we need to analyze the forces acting on the block and use Newton's second law of motion.
First, let's break down the forces acting on the block:
1. The applied force: This force is acting at an angle of 55.0° with the horizontal and has a magnitude of 85.0 N. We can decompose it into its horizontal and vertical components:
F_applied_horizontal = F_applied * cos(angle)
F_applied_vertical = F_applied * sin(angle)
2. The force of kinetic friction: This force opposes the motion of the block and acts in the opposite direction of its motion. Its magnitude can be calculated using the equation:
F_friction = coefficient of kinetic friction * Normal force
Now, let's analyze the Normal force:
In this case, the Normal force is the force exerted by the ceiling on the block perpendicular to the ceiling's surface. Since the block is on the ceiling, there is no vertical acceleration. Therefore, the sum of the vertical forces must be zero:
ΣF_vertical = F_applied_vertical + F_normal - mg = 0
Since the block is not accelerating vertically, the Normal force equals the weight of the block:
F_normal = mg
Now, let's determine the mass and weight of the block:
mass (m) = 3.20 kg
acceleration due to gravity (g) = 9.8 m/s^2
weight of the block = mg
Next, let's find the horizontal force equation:
Using Newton's second law, we can relate the net horizontal force to the mass and acceleration:
ΣF_horizontal = ma
The net horizontal force is given by the sum of the applied force and the force of kinetic friction:
ΣF_horizontal = F_applied_horizontal - F_friction
Finally, let's solve for the coefficient of kinetic friction:
F_friction = coefficient of kinetic friction * Normal force
Rearranging the equation and inserting the known values, we have:
coefficient of kinetic friction = F_friction / F_normal
Substituting the previously derived equations, we get:
coefficient of kinetic friction = (F_applied_horizontal - m * a) / (m * g)
Plug in the given values for the applied force, angle, mass, and acceleration to calculate the coefficient of kinetic friction.
To determine the coefficient of kinetic friction between the block and the ceiling, we need to understand how the normal force works in this case. The normal force is the force exerted by a surface perpendicular to the contact surface. In this situation, since the block is being pushed along the ceiling, the normal force will act in a direction perpendicular to the ceiling.
To determine the normal force, we can use Newton's second law, which states that the sum of the forces acting on an object is equal to the mass of the object times its acceleration. In this case, the only horizontal force acting on the block is the kinetic friction force. The vertical forces acting on the block are the weight (mg) and the normal force (N).
Since the block is moving horizontally along the ceiling, the vertical acceleration is zero. This means that the sum of the vertical forces must be equal to zero. Therefore, the normal force (N) is equal in magnitude and opposite in direction to the weight of the block (mg).
Now, we can calculate the normal force. We'll use the equation:
N - mg = 0
Rearranging the equation, we have:
N = mg
where m is the mass of the block and g is the acceleration due to gravity (9.8 m/s^2).
Given that the mass of the block is 3.20 kg, we can calculate the normal force:
N = 3.20 kg * 9.8 m/s^2 = 31.36 N
Now that we know the normal force, we can calculate the kinetic friction force using the equation:
fk = μk * N
where fk is the kinetic friction force and μk is the coefficient of kinetic friction.
Since the block is accelerating to the right, the applied force (85.0 N) must overcome the kinetic friction force. In this case, the applied force is at an angle of 55.0° with the horizontal, so we need to determine the horizontal component of the applied force.
The horizontal component of the applied force can be calculated as:
F_horizontal = F_applied * cos(θ)
where F_applied is the applied force and θ is the angle with the horizontal.
F_horizontal = 85.0 N * cos(55.0°) ≈ 55.05 N
Now, we can determine the kinetic friction force:
fk = 55.05 N
Since the block is accelerating, the frictional force must oppose the motion. Therefore, the direction of the kinetic friction force is opposite to the direction of the applied force.
Now, we can calculate the coefficient of kinetic friction:
μk = fk / N
μk = 55.05 N / 31.36 N ≈ 1.76
Therefore, the coefficient of kinetic friction between the block and the ceiling is approximately 1.76.
Fb = 3.2kg * 9.8 = 31.36N = ver(normal)
force of block.
Fh = 85*cos55 = 48.75N.
Fv = 31.36 + 85*sin55 = 101N = ver. force.
Fn = Fh - uFv = ma,
48.75 - 101u = 3.2 * 7.5 = 24,
48.75 -101u = 24,
-101u = 24 - 48.75,
-101u = -24.75,
u = -24.75 / -101 = 0.245 = coefficient
of friction.
NOTE: Fn = Net force.