A 5.00 kg howler monkey is swinging due east on a vine. It overtakes and grab onto a 6.00 kg monkey also moving east on a second vine. The first monkey is moving at 12.0 m/s at the instant I grabs the second, which is moving at 8.00 m/s. After they join on the same vine, what is their common speed?
Use the following relationship:
M1V1 +M2V2= M3V3
Where
M1=5.00kg
V1=12.0m/s
M2=6.00kg
V2=8.00m/s
M3=5.00kg+6.00kg=11.00kg
and
V3=???
Solve for V3:
(5.00kg*12.0m/s)+(6.00kg*8.00m/s)=(11.00kg)V3
V3=108kg*m/s/11.00kg
V3=9.82 N s
V3=9.82m/s
To solve this problem, we can apply the principle of conservation of momentum. The total momentum before and after the monkeys grab onto each other will be the same.
The momentum of an object is given by the product of its mass and velocity: momentum = mass × velocity.
Before grabbing onto each other, the momentum of the first monkey is given by:
momentum1 = mass1 × velocity1 = 5.00 kg × 12.0 m/s.
The momentum of the second monkey is given by:
momentum2 = mass2 × velocity2 = 6.00 kg × 8.00 m/s.
The total momentum before grabbing is:
total initial momentum = momentum1 + momentum2.
After they grab onto each other, they will have a combined mass of 5.00 kg + 6.00 kg = 11.00 kg.
Let's denote the final velocity of the combined monkeys as v.
The total momentum after grabbing onto each other is:
total final momentum = combined mass × final velocity = 11.00 kg × v.
According to the principle of conservation of momentum, the total initial momentum is equal to the total final momentum:
total initial momentum = total final momentum.
Therefore,
momentum1 + momentum2 = combined mass × final velocity.
Substituting the given values into this equation:
(5.00 kg × 12.0 m/s) + (6.00 kg × 8.00 m/s) = 11.00 kg × v.
Simplifying:
60.0 kg*m/s + 48.0 kg*m/s = 11.00 kg × v.
108.0 kg*m/s = 11.00 kg × v.
To find the final velocity, divide both sides of the equation by 11.00 kg:
v = 108.0 kg*m/s / 11.00 kg.
Calculating the value, we find:
v ≈ 9.82 m/s.
Therefore, the common speed of the monkeys after they join on the same vine is approximately 9.82 m/s.
To find the common speed of the two monkeys after they join on the same vine, you can make use of the principle of conservation of momentum.
The equation for momentum is:
p = m * v
Where:
p is the momentum
m is the mass of the object
v is the velocity of the object
According to the conservation of momentum, the total momentum before the monkeys grab onto each other is equal to the total momentum after they join. In this case, since they are both moving in the same direction, the equation for conservation of momentum becomes:
(m1 * v1) + (m2 * v2) = (m1 + m2) * v
Where:
m1 is the mass of the first monkey
v1 is the velocity of the first monkey
m2 is the mass of the second monkey
v2 is the velocity of the second monkey
v is the common velocity of both monkeys after joining
Plugging in the values:
(5.00 kg * 12.0 m/s) + (6.00 kg * 8.00 m/s) = (5.00 kg + 6.00 kg) * v
(60.0 kg*m/s) + (48.0 kg*m/s) = (11.0 kg) * v
108.0 kg*m/s = 11.0 kg * v
Simplifying:
108.0 kg*m/s = 11.0 kg * v
v = 108.0 kg*m/s / 11.0 kg
v ≈ 9.82 m/s
Therefore, their common speed after joining on the same vine is approximately 9.82 m/s.