# Block sliding down a wedge, all resting on a balance

• dorothy
dorothy
Homework Statement
Hello! I am now working on an exercise which is related to mechanics. I calculated it wrongly. Attached is the answer. I have no idea how to do c(ii), I don’t understand how cos theta is applied in that question. Please explain it to me if you get it. thanks a lot!
Relevant Equations
F=ma
a=mg*sin theta

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Consider the wedge block sliding down on the rough incline. Please answer the following three questions which are an elaboration of the hint in c(ii).
1. What is the magnitude and direction of the net force on the sliding block? It cannot be zero because the block is accelerating.
2. What is the force exerted by the block on the wedge? It must be a 2D vector with horizontal and vertical components.
3. What must be true for the wedge to remain stationary?
Bonus question: What is the reading of the balance when the block is accelerating?

Last edited:
berkeman and MatinSAR

## 1. How does the motion of the block affect the balance reading?

When the block slides down the wedge, it exerts a force on the wedge due to gravity and its acceleration. This force is transferred to the balance, causing a change in the reading. The balance measures the combined weight of the wedge and the block, along with any additional forces due to the block's motion.

## 2. Does the angle of the wedge influence the balance reading?

Yes, the angle of the wedge significantly influences the balance reading. A steeper angle increases the component of gravitational force parallel to the wedge, causing the block to accelerate more rapidly and exert a greater force on the wedge. This, in turn, affects the balance reading.

## 3. What role does friction play in this setup?

Friction between the block and the wedge can significantly alter the dynamics of the system. If friction is present, it opposes the motion of the block, reducing its acceleration. This changes the forces exerted on the wedge and, consequently, the reading on the balance. In a frictionless scenario, the block would slide down more smoothly, leading to a different force distribution.

## 4. How can we calculate the forces involved in this system?

To calculate the forces, we need to consider the gravitational force acting on the block, the normal force exerted by the wedge, and any frictional forces if present. Using Newton's second law, we can resolve these forces into components parallel and perpendicular to the surface of the wedge. By summing these forces and considering the system's acceleration, we can determine the net force on the wedge and the resulting balance reading.

## 5. What happens if the block reaches the bottom of the wedge?

When the block reaches the bottom of the wedge, it comes to rest relative to the wedge. At this point, the forces on the wedge stabilize, and the balance reading reflects the combined weight of the block and the wedge without any additional dynamic forces. The system reaches a new equilibrium, and the balance reading should remain constant if no other external forces act on it.

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