A 40-kg child is standing still on a 10-kg skateboard, which is also at rest. If the child walks to the right at 2 m/s, what is the resulting velocity of the skateboard?
momentum net is zero.
0=40*2 + 10*v
solve for v.
To find the resulting velocity of the skateboard, we need to apply the principle of conservation of momentum.
First, let's calculate the initial momentum of the system. The momentum of an object is given by the product of its mass and velocity:
Initial momentum of the child = mass of the child × velocity of the child
= 40 kg × 2 m/s
= 80 kg⋅m/s
The skateboard is initially at rest, so its initial momentum is zero.
The total initial momentum of the system is equal to the initial momentum of the child:
Total initial momentum = initial momentum of the child
= 80 kg⋅m/s
According to the principle of conservation of momentum, the total momentum before an event is equal to the total momentum after the event. Since there are no external forces acting on the system, momentum is conserved.
After the child starts walking on the skateboard, the total momentum of the system remains the same. Let's assume the resulting velocity of the skateboard is V.
Total final momentum = total initial momentum
= 80 kg⋅m/s
The final momentum consists of the momentum of the child and the momentum of the skateboard:
Final momentum of the child = mass of the child × velocity of the child
= 40 kg × 2 m/s
= 80 kg⋅m/s
Final momentum of the skateboard = mass of the skateboard × velocity of the skateboard
= 10 kg × V
Total final momentum = Final momentum of the child + Final momentum of the skateboard
= 80 kg⋅m/s + 10 kg × V
Since the total final momentum is equal to the total initial momentum, we can set up the following equation:
80 kg⋅m/s + 10 kg × V = 80 kg⋅m/s
Now we can solve for V:
10 kg × V = 0 kg⋅m/s
V = 0 m/s
Therefore, the resulting velocity of the skateboard is 0 m/s.
To find the resulting velocity of the skateboard, you can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, assuming no external forces are acting on the system.
In this case, the initial momentum before the child starts walking is zero since both the child and the skateboard are at rest. After the child starts walking, the final momentum of the system should still be equal to zero since there are no external forces acting on it.
The momentum of an object is given by multiplying its mass by its velocity. Let's assume that the resulting velocity of the skateboard is v (to the right). The momentum of the child before walking is (mass of child) * 0 = 0, and the momentum of the skateboard before walking is (mass of skateboard) * 0 = 0.
After the child starts walking, the momentum of the child is (mass of child) * (velocity of child) = 40 kg * 2 m/s = 80 kg*m/s (to the right). The momentum of the skateboard should be equal in magnitude but opposite in direction to balance out the total momentum. So, the momentum of the skateboard is -(mass of child) * (velocity of child) = -40 kg * 2 m/s = -80 kg*m/s (to the left).
Since momentum is conserved, the final momentum of the system is 0 kg*m/s, meaning the resulting momentum of the child and skateboard combined should be equal to zero. Therefore, the resulting velocity of the skateboard can be calculated by dividing the total momentum by its mass.
(velocity of skateboard) * (mass of skateboard) = -(velocity of child) * (mass of child)
(v) * 10 kg = -2 m/s * 40 kg
10v = -80
v = -8 m/s
The resulting velocity of the skateboard is -8 m/s to the left.