a person stands in the center of a frozen pond wearing ice skates. his total weight including his skates is 400 n. he pushes on of his 20 n skates forward at 10 m/s. what is his velocity?
You can't solve this with conservation of momentum, as his leg is attached to his body, and if his body has momentum, the leg moves with the body, and the skates move with the leg.
Now if his skate is detached, and then moved one direction and let go, then
momentum coservation can be used.
skatemass*skate velocity+personmass*personvelocty=0
20*10+(400-20)Vman=0
solve for Vman. Notice it is negative, meaning the opposite direction of the skate.
To find the person's velocity after pushing one of his skates forward, we can use the principle of conservation of linear momentum.
The equation for linear momentum is given by:
p = m * v
where:
p is the momentum,
m is the mass of the object, and
v is the velocity of the object.
Given that the total weight of the person including the skates is 400 N and one of the skates has a force of 20 N, we can determine the mass of the person. Weight is simply the force of gravity acting on an object, so the weight can be calculated as:
weight = mass * acceleration due to gravity
400 N = mass * 9.8 m/s^2
By rearranging the equation, we can solve for mass:
mass = 400 N / 9.8 m/s^2
mass ≈ 40.82 kg
Now we have the mass of the person, we will use this to find the initial momentum of the person before pushing the skate:
initial momentum = mass * initial velocity
Since the person is initially at rest, the initial velocity is zero, so the initial momentum is also zero.
Now, let's find the velocity of the person after pushing the skate forward. According to the principle of conservation of momentum:
initial momentum = final momentum
0 = final momentum
Since there is no external force acting on the person-skate system, the momentum is conserved. Therefore:
final momentum = mass * final velocity
The mass of the person remains the same, but the skate is now moving in the forward direction with a new velocity. Let's denote this velocity as v.
final momentum = 40.82 kg * v
Since the momentum is conserved, the final momentum is zero, so:
0 = 40.82 kg * v
Solving for v:
v = 0 m/s
Thus, the person's velocity after pushing one of his skates forward is zero.