Ball hitting block, elastic collision

[geauxKTM]

Homework Statement

.500kg ball attached to a cord that is 70 cm long. ball strikes a 2.5kg block at rest

what is the speed of the ball just before hitting the block
and collison is perfectly elastic find speed of ball and block after collision

Homework Equations

The Attempt at a Solution

Uo=MGY
(.5)(9.8)(.7)= 3.43J
Ko=0
Uf=0
J=.5(.5)v^2= 2.62

part b
2.62=V2f-V1f
1.31=.5V1f+2.5V2f

matrix on calc
V1f= -1.75
V2f=.87

 

[ideasrule]

I don't understand the question. Do you have a diagram? How is the cord attached? Is it a spring or something?

 

[kerimek]

I would approach this problem by first identifying the relevant equations and principles that can be used to solve it. In this case, we can use the conservation of energy and momentum principles to find the speed of the ball before and after the collision.

Using the conservation of energy principle, we can equate the initial potential energy (Uo) to the final kinetic energy (Kf) of the system. Uo represents the potential energy of the ball due to its height above the ground, while Kf represents the kinetic energy of the ball and block after the collision. This can be represented by the equation Uo = Kf.

Next, we can use the conservation of momentum principle to equate the initial momentum (Po) to the final momentum (Pf) of the system. Po represents the momentum of the ball before the collision, while Pf represents the momentum of the ball and block after the collision. This can be represented by the equation Po = Pf.

Using these principles and the given information, we can solve for the initial speed of the ball (V1i) and the final speeds of the ball (V1f) and block (V2f). Plugging in the values, we get V1i = 3.43 m/s, V1f = -1.75 m/s, and V2f = 0.87 m/s.

Since the collision is perfectly elastic, we can also use the equation for elastic collision, which states that the relative speed of the two objects before and after the collision is the same. This means that the final speed of the ball (V1f) and block (V2f) after the collision will be equal.

In conclusion, the speed of the ball just before hitting the block is 3.43 m/s, and the speeds of the ball and block after the collision are -1.75 m/s and 0.87 m/s, respectively. This calculation shows that the collision is perfectly elastic, as the relative speed of the two objects remains the same before and after the collision.