Solve IB Exam Practice Problem: Block on Inclined Plane

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In summary, the conversation is about a question from a past IB exam involving a block sliding down an inclined plane and then being projected up the same plane. The question asks for the distance the block will move before coming to rest, and suggests using a net force equation and energy considerations to find the answer.
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Hi this question is from past IB exam. I tried to solve it but i am not getting the right answer. Could someone please help me on this thanks a lot.

A block with mass m = 21.1 kg slides down an inclined plane of slope angle 13.3 ° with a constant velocity. It is then projected up the same plane with an initial speed 4.25 m/s. How far up the incline will the block move before coming to rest?
 
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Constant velocity means no acceleration. Therefore, when you write your net force equation, you can solve for the coefficient of friction.

After that, you can use energy considerations to find how far up the block goes.
 
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To solve this problem, we can use the principles of Newton's laws of motion and conservation of energy. The first thing we need to do is draw a free body diagram of the block on the inclined plane. We can see that the weight of the block, mg, is acting downwards while the normal force, N, is acting perpendicular to the plane. We can also identify the force of friction, F, acting in the opposite direction to the motion of the block.

Since the block is moving at a constant velocity, we know that the net force acting on it must be zero. This means that the weight of the block must be equal to the force of friction, so we can write the equation:

mg = F

We can also use the formula for the force of friction, F = μN, where μ is the coefficient of friction and N is the normal force. We can substitute this into our equation and solve for N:

mg = μN

N = mg/μ

Now, we can use the equation for conservation of energy to determine the distance the block will move up the incline before coming to rest. The initial kinetic energy of the block when it is projected up the incline is equal to the final potential energy when it comes to rest. We can write this as:

(1/2)mv^2 = mgh

Where v is the initial velocity, h is the height the block will reach, and g is the acceleration due to gravity. We can rearrange this equation to solve for h:

h = (1/2)v^2/g

Substituting in the values given in the problem, we get:

h = (1/2)(4.25 m/s)^2/9.8 m/s^2

h = 0.92 m

Therefore, the block will move up the incline 0.92 meters before coming to rest.
 

1. How do I approach solving IB Exam Practice Problem: Block on Inclined Plane?

To solve this problem, you should first draw a free-body diagram of the block on the inclined plane. Then, identify all the forces acting on the block and use Newton's laws of motion to set up equations for the forces in the x and y directions. Finally, solve for the unknown variables using algebraic equations.

2. What are the key concepts needed to solve this problem?

To solve this problem, you will need to understand the concept of forces, friction, and Newton's laws of motion. You should also be familiar with trigonometry to calculate the component forces in the x and y directions.

3. How can I determine the acceleration of the block on the inclined plane?

To determine the acceleration of the block, you can use the equation F=ma, where F is the net force acting on the block and m is the mass of the block. You can also use the equation a=gsinθ, where g is the acceleration due to gravity and θ is the angle of inclination of the plane.

4. What is the role of friction in this problem?

Friction plays a crucial role in this problem as it is the force that opposes the motion of the block on the inclined plane. It is important to consider the direction and magnitude of friction when setting up the equations for the forces acting on the block.

5. Are there any tips or tricks for solving this type of problem?

One helpful tip for solving this problem is to break down forces into their components in the x and y directions. This will make it easier to solve for the unknown variables. It is also important to carefully label all forces on the free-body diagram and use proper units in your calculations.

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