A 3.90 kg block is in equilibrium on an incline
of 27.5◦
.
The acceleration of gravity is 9.81 m/s
2
.
What is Fn of the incline on the block?
Answer in units of N
Fn = m*g*cos27.5
Why did the incline check the block's ID? Because it wanted to know its Fn number!
Fn, or the normal force of the incline on the block, can be calculated using the equation:
Fn = m * g * cos(θ)
where:
m is the mass of the block (3.90 kg),
g is the acceleration due to gravity (9.81 m/s^2), and
θ is the angle of the incline (27.5 degrees).
Plugging in the values, we get:
Fn = 3.90 kg * 9.81 m/s^2 * cos(27.5 degrees)
And the answer is... *drumroll*... the normal force Fn of the incline on the block is approximately in units of N!
To find the normal force (Fn) of the incline on the block, we need to analyze the forces acting on the block.
On an inclined plane, the weight (W) of the object can be resolved into two components: one parallel to the incline (W_parallel) and one perpendicular to the incline (W_perpendicular).
The perpendicular component of the weight (W_perpendicular) acts against the normal force (Fn) of the incline on the block.
Since the block is in equilibrium, the accelerations along the x and y directions are zero.
The equation for the perpendicular component of the weight is:
W_perpendicular = W * cos(theta)
Where:
- W is the weight of the block, given by W = m * g, where m is the mass of the block and g is the acceleration due to gravity.
- cos(theta) is the cosine of the angle of inclination (27.5 degrees).
Let's calculate the normal force (Fn) using the given values.
First, calculate the weight of the block:
W = m * g
W = 3.90 kg * 9.81 m/s^2
W = 38.259 N
Now, calculate the perpendicular component of the weight:
W_perpendicular = W * cos(theta)
W_perpendicular = 38.259 N * cos(27.5 degrees)
W_perpendicular = 34.529 N
Therefore, the normal force (Fn) of the incline on the block is approximately 34.529 N.
To find the normal force (Fn) exerted by the incline on the block, we need to understand the forces acting on the block in equilibrium. In this case, there are two forces acting on the block: the force of gravity (Fg) and the normal force (Fn).
The force of gravity acts vertically downward and can be calculated as the product of the mass of the block (m) and the acceleration due to gravity (g).
Fg = m * g
Given that the mass of the block is 3.90 kg and the acceleration due to gravity is 9.81 m/s^2, we can calculate Fg:
Fg = 3.90 kg * 9.81 m/s^2
Next, we need to consider the incline angle (θ) to determine the direction of the normal force. The normal force acts perpendicular to the surface of contact between the block and the incline.
Since the block is in equilibrium, the normal force and the force of gravity have the same magnitude but act in opposite directions along the incline.
Therefore, the normal force can be calculated as:
Fn = Fg * cos(θ)
Substituting the given values, we have:
Fn = (3.90 kg * 9.81 m/s^2) * cos(27.5°)
Now, you can use a calculator to find the value of Fn.