Modelling the height of a block up a slope with time

• oMattz
In summary, the problem involves a block of mass M1 on a rough slope attached to another mass M2 by a string passing over a frictionless pulley. The goal is to find an expression for the height of the block above the bottom of the slope as a function of time, considering different values of the parameters. The equations used include F(gravity down slope) = mgsin(theta), F(friction down slope) = umgcos(theta), f=ma, and s = ut +1/2at^2. The solution involves analyzing the forces on each mass separately and taking into account the possibility of both masses accelerating.
oMattz

1. Homework Statement

A block, of mass M1, on the rough slope shown is attached to another mass M2 by a light, inextensible string which passes over a frictionless pulley as shown in the diagram (the coefficient of friction between the block and the slope is u ). The block is released from rest. Find an expression for the height of the block above the bottom of the slope as a function of time. (You should consider the full range of behaviour that may happen for different values of the parameters).

Homework Equations

[/B]
F(gravity down slope) = mgsin(theta)
F(friction down slope) = umgcos(theta)
f=ma
s = ut +1/2at^2

The Attempt at a Solution

Force of gravity on block is m1gsin(theta)
Force of friction on block is um1gcos(theta)
Force needed to push block up slope at constant speed = m1gsin(theta) + um1gcos(theta)
If M2g > Force needed then block will accelerate up slope with a=(M2g-(m1gsin(theta) + um1gcos(theta)))/m1
vertical component of that acceleration = asin(theta)
height = ut + 1/2at^2
height = 0.5*(m2g-(m1gsing(theta) + um1gcos(theta)))/m1)sin(theta)*t^2
I'm pretty sure this answer is wrong as it is so complex, but would just like either confirmation that it is right/wrong and where to go

oMattz said:
Force of friction on block is um1gcos(theta)
The problem statement does not discriminate static and kinetic coefficients, but it does ask you to consider all possibilities. What would be a more circumspect statement than the above?
oMattz said:
If M2g > Force needed then block will accelerate up slope
True. What if it isn't, though?
oMattz said:
with a=(M2g-(m1gsin(theta) + um1gcos(theta)))/m1
Don't forget M2 will accelerate too. Consider the tension and analyse the forces on each mass separately.

1) How does the height of a block change over time when it is pushed up a slope?

The height of a block will decrease as it is pushed up a slope, as the slope acts against the force of gravity on the block, causing it to lose potential energy and decrease in height.

2) What factors affect the rate of change in the height of the block?

The rate of change in the height of the block is affected by the angle of the slope, the mass of the block, and the force applied to push the block up the slope.

3) Can you create a mathematical model to represent the relationship between height and time for a block moving up a slope?

Yes, a mathematical model can be created using the equations for force, work, and energy to represent the relationship between height and time for a block moving up a slope.

4) How accurate is the model for predicting the height of a block at any given time?

The accuracy of the model depends on the accuracy of the input parameters and the assumptions made in the model. It is important to validate the model with real-world data to ensure its accuracy.

5) Can this model be applied to different types of slopes and blocks?

Yes, the model can be applied to different types of slopes and blocks as long as the input parameters are adjusted to match the specific conditions of the slope and block being studied.

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