Hellow I have questiones in physics,
it's google translate so my be it's not so easy. But thanks for the help
A weight with mass (m2) = 28 kg hanging from a rope.
The rope runs over a frictionless pulley and attached to a box of mass m1 = 52 kg.
The box is on a inclined plane with endpoints in A. Oblique either by angle v = 180 in relation to the horizontal.
The friction coefficient between the box m1 inclined plane is ì = 0.2.
The length of the inclined plane from A to snaffle is great and always so large that the assumptions in the problem can be solved. The rope has always large enough length to keep the distance between the cage and pulley.
Assume that the rope is very smooth and slippery, and that both it and the pulley can be considered weightless (mass resolving) in this task.
Look away from time to tensioning of the rope,
assume that there is tight
b) After a time t = 3s blow (cut) the rope.
What is the speed of the system then?
How far have the box and the weight shifted when this happens?
c) Will the box stop now as a result of the rope is cut? (Explain and show)
If so, for how long after the rope broke, and how
far, the fund total moved on before it stops?
d) Assume that there is sufficient free height of fall of the weight that it can fall freely throughout the time it takes to fund a halt.
How far has the lot fell in total - including the time it was tied to checkout
above?
To solve this problem, we can break it down into different parts. Let's start with part b).
b) After cutting the rope, the box and weight will continue to move downwards due to the force of gravity. The tension in the rope before cutting was balancing the weight and the box. After cutting, there will be no tension to oppose the weight, so it will fall freely under the force of gravity.
To find the speed of the system after cutting the rope, we need to use the principle of conservation of energy.
The potential energy of the system before cutting the rope can be given by:
Potential energy = mass of the box * acceleration due to gravity * height
In this case, the height is the distance between the initial position of the box and the snaffle point.
The kinetic energy of the system after cutting the rope can be given by:
Kinetic energy = (mass of the box + mass of the weight) * velocity^2 / 2
Since the system is initially at rest, the initial kinetic energy is zero.
According to the conservation of energy, the potential energy before cutting the rope should be equal to the kinetic energy after cutting the rope. So, we can set up the equation:
(m1 * g * h) = ((m1 + m2) * v^2) / 2
Here, g is the acceleration due to gravity (approximately 9.8 m/s^2), and v is the final velocity of the system after cutting the rope.
To find the velocity, we can rearrange the equation and solve for v:
v^2 = (2 * m1 * g * h) / (m1 + m2)
Now we can substitute the values given in the problem.
m1 = 52 kg
m2 = 28 kg
h = height of the inclined plane
Let's assume the angle of the inclined plane is theta.
The height of the inclined plane can be calculated using the formula:
h = L * sin(theta)
L is the length of the inclined plane from point A to the snaffle point. Since it is mentioned that the length is large enough, we can assume it is infinitely long and the box will move infinitely far.
Substituting the known values, we have:
h = L * sin(180) = L * sin(π) = 0
Therefore, the height of the inclined plane is 0 and the velocity of the system after cutting the rope will also be 0.
Now let's move on to part c).
c) Since the velocity of the system after cutting the rope is 0, the box will come to a stop. This is because the friction between the box and the inclined plane (with a coefficient of friction μ = 0.2) will act as the opposing force.
The box will continue to move for a certain distance after the rope is cut until it comes to a stop. To find this distance, we can use the equation:
frictional force = coefficient of friction * normal force
The normal force can be calculated as:
normal force = mass of the box * acceleration due to gravity * cos(theta)
The frictional force can be given by:
frictional force = mass of the box * acceleration due to gravity * μ
Since the frictional force opposes the motion, we can set up the equation:
frictional force = mass of the box * acceleration
Substituting the expressions for the frictional force, normal force, and acceleration, we have:
mass of the box * acceleration due to gravity * μ = mass of the box * acceleration due to gravity * cos(theta)
Simplifying the equation, we get:
μ = cos(theta)
Since the value of μ is 0.2, we can find the value of theta as follows:
cos(theta) = 0.2
theta ≈ acos(0.2)
Using a calculator, we can find the value of theta to be approximately 78.46 degrees.
Therefore, the box will stop after moving a certain distance on the inclined plane, which corresponds to the length of the inclined plane from point A to the position where the box comes to a stop.
To answer these questions, we will analyze the situation step by step:
Step 1: Find the acceleration of the system:
Since the pulley is frictionless, the tension force in the rope is the same on both sides. We can write down Newton's second law for the box and the weight:
m1 * a = m1 * g * sin(v) - T (1)
m2 * a = T - m2 * g (2)
Where m1 is the mass of the box, m2 is the mass of the weight, a is the acceleration, g is the acceleration due to gravity (approximately 9.8 m/s^2), T is the tension force, and v is the angle of the inclined plane.
Now let's solve these equations simultaneously to find the acceleration a.
Step 2: Find the speed after the rope is cut (t = 3s):
We can use the equation of motion to find the speed of the system after 3 seconds. The equation is:
v = u + a * t
Where v is the final velocity, u is the initial velocity (which is assumed to be zero in this case), a is the acceleration, and t is the time.
Step 3: Find the distance traveled by the box and the weight when the rope is cut:
To find the distance traveled, we can use the equation of motion for distance:
x = u * t + 0.5 * a * t^2
Where x is the distance, u is the initial velocity, a is the acceleration, and t is the time.
Step 4: Determine if the box will stop after the rope is cut:
If the box stops, it means the net force on the box is zero. We can calculate the net force as the sum of the weight component down the incline and the friction force opposing the motion:
Net force = m1 * g * sin(v) - ì * m1 * g * cos(v)
If the net force is zero, the box will stop. Otherwise, it will continue moving.
Step 5: Calculate the time and distance traveled before the box stops:
If the box stops, we can use the equation of motion to find the time and distance traveled before it stops. The equation is:
v = u + a * t
Where v is the final velocity (which is assumed to be zero when the box stops), u is the initial velocity, a is the acceleration, and t is the time.
Step 6: Find the total distance the weight has fallen:
If the weight can fall freely during the entire time, we can use the equation of motion for distance:
x = 0.5 * g * t^2
Where x is the distance, g is the acceleration due to gravity, and t is the time.
By following these steps and plugging in the given values, you can find the answers to the questions b), c), and d) in this physics problem.