A steel block is resting on a Flat plank 6m long ,and how high can one end of a plank be lifted For the block to start to move,if the coeficient of friction is 0.3
Fp = mg*sin A = Force parallel to the
incline.
Fn = mg*Cos A = Normal = Force perpendicular to the incline.
Fs = u*Fn = Force of static friction.
Fp-Fs = 0
Fp = Fs
mg*sin A = u*mg*Cos A
Divide both sides by mg*Cos A:
sin A/Cos A = u = 0.3
sin A/Cos A = Tan A
Tan A = 0.30
A = 16.7o
h = L*sin16.7 = 6*sin16.7 = 1.72 m.
I feel like the weight of the steel block has to be given in order to solve this problem…
To determine the maximum height that one end of the plank can be lifted for the steel block to start moving, we need to consider the force of friction between the block and the plank.
The force of friction can be calculated using the formula:
Force of friction = coefficient of friction * normal force
The normal force, in this case, is equal to the weight of the steel block, which can be calculated using the formula:
Weight = mass * acceleration due to gravity
Since the steel block is resting on the plank and not moving vertically, the weight is balanced by the normal force:
Weight = Normal force
Therefore, the force of friction can be written as:
Force of friction = coefficient of friction * weight
Now, let's calculate the maximum force of friction that the steel block can experience before it starts to move:
1. Calculate the weight of the steel block:
- Determine the mass of the steel block.
- Multiply the mass by the acceleration due to gravity (9.8 m/s²).
2. Calculate the maximum force of friction:
- Multiply the coefficient of friction by the weight.
3. Calculate the height that one end of the plank can be lifted:
- Divide the maximum force of friction by the weight of the steel block.
- Multiply the result by the length of the plank.
Let's calculate it step by step!
Step 1: Calculate the weight of the steel block
Let's say the mass of the steel block is 10 kg.
Weight = mass * acceleration due to gravity = 10 kg * 9.8 m/s² = 98 N
Step 2: Calculate the maximum force of friction
Force of friction = coefficient of friction * weight
Maximum force of friction = 0.3 * 98 N = 29.4 N
Step 3: Calculate the height that one end of the plank can be lifted
Height = (maximum force of friction / weight) * length of the plank
Height = (29.4 N / 98 N) * 6 m = 1.8 m
Therefore, one end of the plank can be lifted up to a maximum height of 1.8 meters for the steel block to start moving.
To find out how high one end of the plank can be lifted for the steel block to start to move, we need to consider the force of friction between the block and the plank.
The force of friction can be calculated using the formula:
Friction force (Ff) = coefficient of friction (μ) * normal force (N)
The normal force is equal to the weight of the block, which can be calculated by multiplying the mass of the block (m) by the acceleration due to gravity (g).
Normal force (N) = mass of block (m) * acceleration due to gravity (g)
Once we have the friction force, we can determine the maximum angle at which the block will start to move using the equation:
θ = arctan(Ff / N)
Now let's calculate the maximum height that one end of the plank can be lifted:
1. Calculate the weight of the block:
- Find the mass of the steel block.
- Multiply the mass by the acceleration due to gravity (approximately 9.8 m/s^2) to get the weight.
2. Calculate the normal force:
- Multiply the weight of the block by the cosine of the angle at which the plank is lifted.
3. Calculate the friction force:
- Multiply the coefficient of friction (0.3) by the normal force.
4. Calculate the maximum angle (θ) at which the block will start to move:
- Use the inverse tangent function (arctan) to find the angle at which the friction force equals the normal force.
5. Calculate the maximum height:
- Multiply the length of the plank (6m) by the sine of the maximum angle.
By following these steps, you can determine the maximum height one end of the plank can be lifted for the steel block to start to move.