# Block on an accelerating wedge

• housemartin
In summary, a 45o wedge is pushed along a table with constant acceleration. A block of mass slides without friction on the wedge and is subject to the force of gravity directed down. The only forces as seen by an inertial observer are mg (the force of gravity) and N (the normal force). To associate the accelerations of x and y in an inertial frame, x (acceleration A) is position of the wedge and y (acceleration B) is position of the block. The acceleration of x' in the non-inertial frame is then added to the acceleration of the block in the inertial frame. The equation for the net force on the block is found by solving equations (1) and
housemartin
Hello,

## Homework Statement

A 45o wedge is pushed along a table with constant acceleration A. A block of mass m slides without friction on the wedge. Find its acceleration in y direction. (Gravity directed down, acceleration due to gravity is g).
[PLAIN]http://img210.imageshack.us/img210/6958/wedge45.jpg

## Homework Equations

if i make x' be a horizontal coordinate moving with wedge, then this is in not inertial frame so -mA term adds:
$$m \frac{d^2 x'}{dt^2} = F_x - mA = N cos(\theta) - mA$$ (1)
y coordinate is inertial, and Newton second law is:
$$m \frac{d^2 y}{dt^2} = F_y = N sin(\theta) - mg$$ (2)
The only forces as seen by inertial observer are mg and normal force N.
To associate accelerations of x and y in inertial frame I make X (acceleration A) to be position of wedge and x that of block, then:
$$-\frac{d^2 y}{dt^2} = (\frac{d^2 x}{dt^2}-A)tan(\theta)$$ (3)
sins theta = 45, tan(45)=1

## The Attempt at a Solution

Solving equations (1) and (2) for N, and dividing one by another, i get:
$$tan(\theta)(\frac{d^2 x'}{dt^2}+A) = (\frac{d^2 y}{dt^2} + g)$$
Since acceleration of x' in not inertial frame plus A is acceleration of block in inertial frame, and tan(45) = 1, i get:
$$\frac{d^2 x}{dt^2} = \frac{d^2 y}{dt^2} + g$$
Combining this with equation (3), i get:
$$\frac{d^2 y}{dt^2} = (A - g)/2$$
Is my solution correct? The fact that when A>g block is moving up kinda confuses me. Sorry for my english.

Last edited by a moderator:
dude, the answer is ay= |g-A| /2

it can be brought by simply using the pseudo force on the block.

bikramjit das is right ... just use pseudo force ... pseudo forces come into action when tyou need to apply Newton's laws in non inertial frame ... F(pseudo) = -ma
m is mass of body on which Newton's laws are to be applied and a is acc. of frame ((the bigger block)

note F is opposote to a

well i made few mistakes in my solution, forgot to divide by two and mixed + and - sign in one place. So my final answer is ay = (A-g)/2. What is pseudo i don't know ;] if it's F = -mA, this is kinda way i did this problem. Just i have no idea how to bring this in a simple way.

wat u did is conventional. but pseudo force takes place when the system is in non- inertial frame of ref. Refer google with the term "pseudo force", u'll definitely get what I am trying to say

ok, thank you both for help.

## 1. What is a block on an accelerating wedge?

A block on an accelerating wedge is a physics problem where a block is placed on top of a wedge that is accelerating horizontally. The block is subject to both the force of gravity and the acceleration of the wedge, creating a unique system.

## 2. How is the acceleration of the block on an accelerating wedge calculated?

The acceleration of the block on an accelerating wedge can be calculated using Newton's Second Law of Motion, which states that force is equal to mass times acceleration (F=ma). The forces acting on the block (gravity and the normal force from the wedge) can be used to calculate the acceleration of the block.

## 3. What is the relationship between the angle of the wedge and the acceleration of the block?

The angle of the wedge directly affects the acceleration of the block. As the angle of the wedge increases, the acceleration of the block decreases. This is because the component of the force of gravity pulling the block down the wedge decreases as the angle increases.

## 4. How does the weight of the block affect its acceleration on an accelerating wedge?

The weight of the block, also known as its mass, does not affect its acceleration on an accelerating wedge. This is because the mass of the block is cancelled out in the equation for acceleration (F=ma). However, the weight of the block does affect the normal force acting on the block, which in turn affects its acceleration.

## 5. What is the significance of studying a block on an accelerating wedge?

Studying a block on an accelerating wedge allows for a better understanding of the principles of Newton's laws of motion and forces. It also has practical applications in real-life scenarios, such as understanding the motion of objects on inclined planes and the design of machines and vehicles that use wedges for lifting and moving objects.

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