Ball hitting block, elastic collision

• geauxKTM
In summary, an elastic collision is a type of collision where kinetic energy is conserved and the total momentum of the objects remains the same before and after the collision. The mass of the objects affects the outcome of an elastic collision by determining the amount of kinetic energy and momentum each object will have. The formula for calculating the velocity of an object after an elastic collision is v = (m1u1 + m2u2)/(m1 + m2). Energy cannot be lost in an elastic collision, as per the law of conservation of energy.
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

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

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

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.

What is an elastic collision?

An elastic collision is a type of collision where kinetic energy is conserved. This means that the total kinetic energy of the objects before the collision is equal to the total kinetic energy after the collision.

What happens to the momentum of the objects in a ball hitting block, elastic collision?

The momentum of the objects in an elastic collision is conserved. This means that the total momentum of the objects before the collision is equal to the total momentum after the collision.

How does the mass of the objects affect the outcome of a ball hitting block, elastic collision?

The mass of the objects affects the outcome of an elastic collision by determining the amount of kinetic energy and momentum each object will have. Objects with larger mass will have more momentum and kinetic energy compared to objects with smaller mass.

What is the formula for calculating the velocity of an object after a ball hitting block, elastic collision?

The formula for calculating the velocity of an object after an elastic collision is v = (m1u1 + m2u2)/(m1 + m2), where v is the final velocity, m1 and m2 are the masses of the objects, and u1 and u2 are the initial velocities of the objects.

Can energy be lost in an elastic collision?

No, energy cannot be lost in an elastic collision. As per the law of conservation of energy, the total energy of a closed system remains constant. In an elastic collision, the kinetic energy is converted into potential energy and vice versa, but the total energy remains the same.

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