Find the impulse exerted on the wedge by the ground during impact

In summary, the net vertical impulse on the wedge should be zero, as seen in the figure. The ground exerts an impulse of ##J cos 30°## on the wedge. However, the given answer is ##J sin 30°##, which is incorrect according to the problem.
  • #1
baldbrain
236
21
Homework Statement
This is a lengthy question with many sub-parts but I have a doubt about just one of them.
A ball of mass 1 kg falling vertically downwards with a velocity of 2 m/s strikes a wedge of mass 2 kg kept on a smooth horizontal surface. The given figure shows the motion of the ball during impact. Find the impulse on the wedge from the ground during impact.
Relevant Equations
None
15608384772188975631598041741577.jpg

Now, the net vertical impulse on the wedge should be zero. It's quite obvious from the figure that the ground will also exert an impulse of ##J cos 30°## on the wedge. But they've given the answer as ##J sin 30°##.
They're wrong, right?
 
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  • #2
baldbrain said:
But they've given the answer as ##J sin 30°##.
They're wrong, right?
Yes, it’s the cos, but everything in the image you posted looks right. Where do they say it is sin?
 
  • #3
haruspex said:
Yes, it’s the cos, but everything in the image you posted looks right. Where do they say it is sin?
At the end of the problem (not in this image). As I said, it has many sub-parts.
Thanks for the clarification.
 

1. What is impulse?

Impulse is the change in momentum of an object over a period of time. It is calculated by multiplying the force applied to an object by the time it takes for the force to be applied.

2. What is a wedge?

A wedge is a simple machine with a triangular shape that is used to push or split objects apart. It is made up of two inclined planes joined together at the narrow end.

3. How is impulse exerted on a wedge during impact?

During impact, the ground exerts a force on the wedge in the opposite direction of its motion. This force, multiplied by the time of impact, gives the impulse exerted on the wedge by the ground.

4. What factors can affect the impulse exerted on a wedge by the ground during impact?

The force of impact, the angle of the wedge, and the material properties of both the wedge and the ground can all affect the impulse exerted on the wedge during impact.

5. Why is it important to consider impulse in wedge design?

Understanding the impulse exerted on a wedge during impact is crucial in designing efficient and effective wedges for various applications. It can help determine the necessary force and angle of the wedge to achieve a desired outcome, as well as inform material choices for durability and safety.

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