A 0.500 kg block is sitting on a horizontal, frictionless surface. The block is connected to a horizontal spring with a force constant of 124 N/m. The other end of the horizontal spring rests against a wall. When a 100.0 g arrow is fired into the wooden block, the spring compresses by 25 cm.
(a) What is the maximum potential energy of the spring?
Ee (at max. compression)= 1/2kx^2
works out to be 3.88 J
Please help with the following..
(b) What was the speed of the arrow and block just after collision?
(c) What was the initial kinetic energy of the arrow?
(d) Explain any difference between (a) and (c).
Thanks for any assistance!
the initial KE of the block/arrow must be the same energy as the PE of the spring, so solve for speed from that.
The arrow hit the block, momentum was conserved
massarrow*speedarrow=(massarrow+block)speed above.
so use that speed to get the KE of the arrow.
The difference? It was an inelastic collision, what happened to the energy?
so what is the answer to b) and c)
the speed was high
To find the speed of the arrow and block just after the collision, we can use the principle of conservation of momentum. This principle states that the total momentum of a system before a collision is equal to the total momentum after the collision, provided no external forces are acting on the system.
In this case, before the collision, the wooden block is at rest, so its momentum is zero. The arrow is moving with an unknown speed, so its momentum is given by mass multiplied by velocity (p = mv).
Let's assume the speed of the arrow and block just after the collision is v. The momentum of the arrow and block system just after the collision is (M + m)v, where M is the mass of the wooden block and m is the mass of the arrow.
Using the principle of conservation of momentum, we can equate the initial momentum to the final momentum:
(m * initial velocity of arrow) = (M + m) * v
Solving for the initial velocity of the arrow:
initial velocity of arrow = [(M + m) * v] / m
Now, let's move on to finding the initial kinetic energy of the arrow.
The equation for kinetic energy is given by:
Kinetic energy (K.E.) = 1/2 * mass * velocity^2
To find the initial kinetic energy of the arrow, we plug in the mass of the arrow and the initial velocity of the arrow into the equation:
Initial kinetic energy of the arrow = 1/2 * m * (initial velocity of arrow)^2
Finally, let's compare the maximum potential energy of the spring (from part a) with the initial kinetic energy of the arrow.
The difference between (a) and (c) arises because they represent different forms of energy. The maximum potential energy of the spring (4 J) represents the energy stored in the compressed spring, while the initial kinetic energy of the arrow represents the energy associated with the motion of the arrow before the collision. These energies are different because they are associated with different physical processes and quantities.