# Dynamics help: Block on a wedge on an incline (frictionless surfaces)

• Engineering
• Pipsqueakalchemist
In summary: It would be helpful if you could walk me through the steps.In summary, you are having trouble with relative motion with moving inclines and you need to use energy and momentum conservation to solve the problem.
Pipsqueakalchemist
Homework Statement
Block B of mass 10-kg rests as shown on the upper surface of a 22-kg wedge A. Knowing that the system is released from rest and neglecting friction, determine (a) the acceleration of B, (b) the velocity of B relative to A at 0.5 s
Relevant Equations
Newton’s 2nd law
Relative motion
So I’m having trouble with relative motion with moving inclines and I literally can’t find any help online and my prof does a lot of these problems. This is one of my homework problems, can anyone help me with it please.

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PeroK said:

According to the homework guidelines, you have to give this your best shot. Put some energy into it!

Well I’ve tried the problem before and I looked over the solutions but I don’t fully understand it. To be specific I know how to set up the FBD but I don’t how to apply the relative motion of the block and the incline.

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Try using energy, rather than forces.

PeroK said:
Try using energy and momentum conservation, rather than forces.
But this for Newton’s 2nd law section so I have to use forces. Do you want to see the solutions and maybe you’ll understand better than me.

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Wished I joined this forum sooner ,my midterm is in a few hours and I kinda just accepted that I’m screwed at this point. Hopefully I can understand this better for the exam

Pipsqueakalchemist said:
But this for Newton’s 2nd law section so I have to use forces. Do you want to see the solutions and maybe you’ll understand better than me.
The diagrams are hard to read. The idea is that you write down all the forces (obviously) then look for physical constraints: in this case the relationship between the motion of the small block and the large block. Then it's a case of solving the simultaneous equations.

The solution looks light on explanation and heavy on numbers to me.

## 1. How do I calculate the acceleration of the block on the wedge on an incline?

The acceleration of the block on the wedge on an incline can be calculated using the formula a = g(sinθ - μcosθ), where g is the acceleration due to gravity, θ is the angle of the incline, and μ is the coefficient of friction between the block and the wedge.

## 2. What is the normal force acting on the block?

The normal force acting on the block is equal to the component of the weight of the block that is perpendicular to the incline. It can be calculated using the formula N = mgcosθ, where m is the mass of the block and θ is the angle of the incline.

## 3. How do I calculate the tension in the string connecting the block and the wedge?

The tension in the string can be calculated using the formula T = mgsinθ, where m is the mass of the block and θ is the angle of the incline. This is assuming that the string is massless and the block is not accelerating in the direction of the string.

## 4. How do I determine the maximum angle of the incline before the block starts to slide?

The maximum angle of the incline before the block starts to slide is known as the angle of repose and can be calculated using the formula tanθ = μ, where μ is the coefficient of friction between the block and the wedge. This assumes that the block is on the verge of sliding and the force of friction is at its maximum.

## 5. Can I neglect the mass of the wedge in my calculations?

In most cases, the mass of the wedge can be neglected as it is usually much larger than the block and has a negligible effect on the system. However, if the mass of the wedge is significant, it should be included in the calculations.

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