can someone help me with this momentum/force/energy problem?

Question

An aluminum block with a mass of 1 kg moves to the left with a constant velocity of 8 meters per second. After striking a spring, the clock is brought to rest in 0.005 second as the spring is compressed.


*a. what is the magnitude of the momentum change of the block in coming to rest?
*b. what is the average force exerted on the spring by the block a the block is brought to rest?
*c. The energy of the spring at its maximum compression is nearly ________.


can you show it step by step please?

Answer 1

a) momentum is P= m x v (mass x velocity)

P = 1kg x 8 m/s = 8 kg m/s

the change in momentum is -8 kg m/s (because it lost momentum)

b) F = M x A (force equals mass x acceleration)

F = 1kg x (-8 m/s / .005 sec)
F= -1600N

(again, the value is negative because we have slowed down the object)

c) Kinetic Energy of a moving object is KE = .5MV^2

so...
KE= 1/2 x 1kg x (8m/s)^2 = 32 joules

The spring has 32 joules of potential energy once the spring is at maximum compression (all kinetic converted to potential energy)

Answer 2

The equation for momentum in mechanics,
p = mv
where
p = momentum
m = mass
v = instantaneouns velocity

therefore, for (a):
change of magnitude in momentum is equilvalent to:
initial momentum - final momentum
= m1 x v1 - m2 x v2
since the mass remains the same, (i.e. m1 = m2)
= m (v1 - v2)
= 1kg x (8m/s - 0 (because it was stopped))
= 1 x 8
= 8 kg m/s

For (b),
Average force exerted on the spring,
from (a), we know that the magnitude of force applied is 8 kg m/s,
and from the question we know that it was brought to rest in 0.005 second,
Hence,
Average Force exeted on spring: 8/ 0.005 = 1600 N

For (c),
The answer is same as (a), 8. This is due to the principle of consevation of momentum. Assuming the system is ideal, i.e. no friction and no ai resistance, then the energy from the block's momentum should be fully transferred to the spring as it is brought to rest.

Answer 3

a. Momentum = mass x velocity
Change in momentum = mass x change in velocity
= 1 kg x 8m/s = 8 kg m/s

b. Force = change in momentum / time
= 8 kg m/s / 0.005 s
= 1600 kg m/s^2 = 1600 N

c. If we assume that - by stopping the mass - the kinetic energy of mass is nearly all changed into potential energy of spring:
Kinetic energy = mass x velocity^2
= 1 kg x (8m/s)^2
= 64 kg m^2/s^2 = 64 J

Answer 4

I think I can start: Momentum is mass x velocity.
1 kg x 8 m/sec = 40 kg-m/sec. As the spring changes the momentum to 0, the change is 40 kg-m/sec.

Force = mass (1 kg) x acceleration ([-8 m/sec]/.005secs) = 1600... Newtons?

The energy of the spring is the potential energy stored up by stopping the block. Therefore, it is equal to the kenetic energy of the moving bleck; which is E = mass x velocity^2 =
1 kg x 8^2 =
1 kg x 64 m/sec = 64 kg-m/sec.

PLEASE DO NOT ACCEPT THIS AS CORRECT WITHOUT CONFIRMATION FROM OTHERS. (It's been a long time!)

Answer 5

a) Δp = m(v - v๐) = 1 kg( 0 m/s - 8 m/s) = -8 kg m/s

b) f = Δp/Δt = -8/5E-3 kg m/s² = -1 600 N. Minus sign indicates force is in the inverse direction as velocity.

c) There's a direct formula (½kx²) to compute energy stored in the spring, but is useless here since you're not given the spring constant k, nor the spring compression, x. But energy is energy, whatever its form, since it is conserved. The kinetic energy lost equals the potential energy gained by spring. Thus,

½mv² = ½ × 1 × 8² = 32 N m, or 32 J

Answer 6

a. Momentum is m*v. When the block has come to rest, its velocity is zero, so its momentum is zero. The change is m*v-0.

b. The block had a kinetic energy of (1/2)*m*v^2. The work the spring did to stop it has to equal that original kinetic energy. The work is Fs*d. So
(1/2)*m*v^2 = Fs*d. Plug in the variables you know and solve for Fs.

c. equal to the original kinetic energy.

Answer 7

a) Calculate initial momentum, which is proportional to speed and weight of block - do not get confused by leftwards or rightwards metaphors, which may not relate at all to keyboard use, or to word clock instead of block. The total time of deceleration to zero speed/momentum (the assumption is that of linear motion) is given by the time which is taken by the spring to compress, so change of momentum must be proportional to this - calculate forces in newtons: the momentum change is assumed to be 100%, i.e. all the energy of motion has been absorbed by the spring.
b) You would need to know about the elasticity of springs, but the time of compression gives the clue as to how this can be solved graphically. Deceleration is in a straight line, but is not linear graphically, so use integration method to find average force in newtons per unit of spring length.
c) Some energy is dissapted as heat, but energy may be estimated as force of same number of newtons as the block orignially had, but in the reverse direction. Energy in practical terms is only explicated as motion, even so, you cannot expect the spring to convert all the stored energy to motion.

Answer 8

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