Hi, having some trouble with a problem, here it is, followed by what I tried...which was wrong...thank you for your help
An automobile of mass 3000 kg is driven into
a brick wall in a safety test. The bumper
behaves like a Hooke’s-law spring. It has an
effective spring constant of 5 × 106 N/m, and
is observed to compress a distance of 1.88 cm
as the car is brought to rest.
What was the initial speed of the automo-
bile?
Answer in units of m/s.
F = -Kx
F = ma
-Kx = ma
-Kx = m(v-v0)
Kx = mv0
5*10e6N/m * .0188m = 3000kg * V0
V0 = 31.3333m/s
But that didn't work
neither did -31.3333m/s
Any help is greatly appreciated, thank you
An automobile of mass 3000 kg is driven into
a brick wall in a safety test. The bumper
behaves like a Hooke’s-law spring. It has an
effective spring constant of 5 × 106 N/m, and
is observed to compress a distance of 1.88 cm
as the car is brought to rest.
What was the initial speed of the automo-
bile?
Answer in units of m/s.
F = -Kx
F = ma
-Kx = ma
-Kx = m(v-v0)
Kx = mv0
5*10e6N/m * .0188m = 3000kg * V0
V0 = 31.3333m/s
But that didn't work
neither did -31.3333m/s
Any help is greatly appreciated, thank you
-
An automobile of mass 3000 kg is driven into a brick wall in a safety test. The bumper behaves like a Hooke’s-law spring. It has an
effective spring constant of 5 × 106 N/m, and is observed to compress a distance of 1.88 cm as the car is brought to rest.
What was the initial speed of the automobile?
As the spring compresses, its potential energy increases 0 to maximum; and the kinetic energy of the car decreases from maximum to 0.
PE = ½ * k * d^2
k = 5 * 10^6 N/m
d = 1.88 cm = 0.0188 m
PE= ½ * 5 *10^6 * 0.0188^2
Assuming energy loss from friction, the maximum KE of the car = maximum PE of spring.
KE of car = ½ * 5 *10^6 * 0.0188^2
½ * 3000 * v^2 = ½ * 5 *10^6 * 0.0188^2
Solve for v = 0.768 m/s
OR
The work done to the spring, as the car compresses it, causes the kinetic energy of the car to decrease to 0.
Work = F * d
F = k * d
The force is not constant. As the spring is compressed, the force increases from 0 N to k * d
So Work = average force * distance
k = 5 * 10^6 N/m
d = 1.88 cm = 0.0188 m
Maximum force = 5 * 10^6 * 0.0188
average force = ½ ( Initial force + Final force) = ½ * (0 + 5 * 10^6 * 0.0188)
Work = (½ * 5 * 10^6 * 0.0188) * 0.0188 = ½ * 5 * 10^6 * 0.0188^2
effective spring constant of 5 × 106 N/m, and is observed to compress a distance of 1.88 cm as the car is brought to rest.
What was the initial speed of the automobile?
As the spring compresses, its potential energy increases 0 to maximum; and the kinetic energy of the car decreases from maximum to 0.
PE = ½ * k * d^2
k = 5 * 10^6 N/m
d = 1.88 cm = 0.0188 m
PE= ½ * 5 *10^6 * 0.0188^2
Assuming energy loss from friction, the maximum KE of the car = maximum PE of spring.
KE of car = ½ * 5 *10^6 * 0.0188^2
½ * 3000 * v^2 = ½ * 5 *10^6 * 0.0188^2
Solve for v = 0.768 m/s
OR
The work done to the spring, as the car compresses it, causes the kinetic energy of the car to decrease to 0.
Work = F * d
F = k * d
The force is not constant. As the spring is compressed, the force increases from 0 N to k * d
So Work = average force * distance
k = 5 * 10^6 N/m
d = 1.88 cm = 0.0188 m
Maximum force = 5 * 10^6 * 0.0188
average force = ½ ( Initial force + Final force) = ½ * (0 + 5 * 10^6 * 0.0188)
Work = (½ * 5 * 10^6 * 0.0188) * 0.0188 = ½ * 5 * 10^6 * 0.0188^2
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