A person is standing on and facing the front of a stationary skateboard while holding a construction brick. The mass of the person is 89.0 kg, the mass of the skateboard is 4.10 kg, and the mass of the brick is 2.50 kg. If the person throws the brick forward (in the direction they are facing) with a speed of 21.0 m/s relative to the skateboard and we ignore friction, determine the recoil speed of the person and the skateboard.
initial momentum=final momentum
0=(89+4.10)V+2.5*21
solve for V. negative sign means opposite direction than the brick went.
Well, this situation sounds like a recipe for some comical chaos! Let's see if we can calculate the recoil speed of our brave skateboarder.
To solve this, we can use the principle of conservation of momentum. The total momentum before throwing the brick should be equal to the total momentum after throwing the brick.
The initial total momentum is:
Initial momentum = (mass of person + mass of skateboard) * initial velocity of person
Now, let's break it down:
Initial momentum = (89.0 kg + 4.10 kg) * 0 m/s (since the person is initially stationary)
After throwing the brick, the person's momentum changes while the skateboard's momentum remains constant. To find the final velocity of the person and skateboard, we equate the total momentum before and after throwing the brick:
Initial momentum = (mass of person + mass of skateboard) * recoil velocity
Rearranging the equation, we get:
Recoil velocity = Initial momentum / (mass of person + mass of skateboard)
Plugging in the values, we have:
Recoil velocity = (89.0 kg + 4.10 kg) * 0 m/s / (89.0 kg + 4.10 kg)
Now, let me pull out my calculator...
*Ding*
Calculating... calculating...
And the final result is... 0 m/s! That's right, the recoil velocity of the person and the skateboard is zero. Looks like our brave adventurer won't be going anywhere after throwing that brick. Stability is preserved, but maybe a little bit less laughter.
To determine the recoil speed of the person and the skateboard, we can use the principle of conservation of momentum.
1. Calculate the initial momentum of the person and the skateboard:
Initial momentum = (mass of person + mass of skateboard) x velocity of person and skateboard
Initial momentum = (89.0 kg + 4.10 kg) x 0 m/s (since both are at rest initially)
Initial momentum = 0 kg·m/s
2. Calculate the momentum of the brick:
Momentum of the brick = mass of the brick x velocity of the brick
Momentum of the brick = 2.50 kg x 21.0 m/s
Momentum of the brick = 52.5 kg·m/s
3. According to the principle of conservation of momentum, the total initial momentum must be equal to the total final momentum.
Final momentum = (mass of person + mass of skateboard + mass of brick) x final velocity of person and skateboard
Final momentum = (89.0 kg + 4.10 kg + 2.50 kg) x final velocity of person and skateboard
Since we know that the final velocity of the brick is 0 m/s (as the person threw it forward), the final velocity of the person and skateboard will be in the opposite direction.
Final momentum = (89.0 kg + 4.10 kg + 2.50 kg) x (-final velocity of the person and skateboard)
4. Equate the initial momentum and final momentum:
0 kg·m/s = (95.6 kg) x (-final velocity of the person and skateboard)
5. Solve for the final velocity of the person and skateboard:
final velocity of the person and skateboard = 0 kg·m/s / 95.6 kg
final velocity of the person and skateboard = 0 m/s
Thus, the recoil speed of the person and the skateboard is 0 m/s.
To determine the recoil speed of the person and the skateboard, we can apply the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant if no external forces act on it.
Step 1: Calculate the initial momentum
The initial momentum of the system is given by the sum of the individual momenta of the person, skateboard, and brick. The momentum is defined as the product of an object's mass and velocity.
Initial momentum = (Mass of person × Velocity of person) + (Mass of skateboard × Velocity of skateboard) + (Mass of brick × Velocity of brick)
Given:
Mass of person (m1) = 89.0 kg
Velocity of person (v1) = 0 m/s (since the person is stationary)
Mass of skateboard (m2) = 4.10 kg
Velocity of skateboard (v2) = 0 m/s (since the skateboard is stationary)
Mass of brick (m3) = 2.50 kg
Velocity of brick (v3) = 21.0 m/s (relative to the skateboard)
Initial momentum = (89.0 kg × 0 m/s) + (4.10 kg × 0 m/s) + (2.50 kg × 21.0 m/s)
Step 2: Calculate the final momentum
After the person throws the brick, both the person and the skateboard will experience a recoil effect. This means their combined momentum must be zero, as the total momentum of the system is conserved.
Final momentum = (Mass of person × Velocity of person) + (Mass of skateboard × Velocity of skateboard) + (Mass of brick × Velocity of brick)
Given:
Final momentum = 0 (since the combined momentum must be zero, due to the recoil effect)
Step 3: Solve for the unknown velocities
Now, we can set the initial momentum equal to the final momentum and solve for the unknown velocities of the person and skateboard.
Initial momentum = Final momentum
(89.0 kg × 0 m/s) + (4.10 kg × 0 m/s) + (2.50 kg × 21.0 m/s) = (89.0 kg × Velocity of person) + (4.10 kg × Velocity of skateboard) + (2.50 kg × 0 m/s)
Simplifying the equation:
(2.50 kg × 21.0 m/s) = 89.0 kg × Velocity of person + 4.10 kg × Velocity of skateboard
52.50 kg·m/s = 89.0 kg × Velocity of person + 4.10 kg × Velocity of skateboard
Step 4: Solve for the unknown velocities algebraically
Now, we need to rearrange the equation to solve for the recoil velocities of the person and skateboard.
Rearranging the equation:
89.0 kg × Velocity of person + 4.10 kg × Velocity of skateboard = 52.50 kg·m/s
Rewriting in terms of the mass of the person and skateboard:
(89.0 kg × Velocity of person) + (4.10 kg × Velocity of skateboard) = 52.50 kg·m/s
Rearranging the terms:
89.0 kg × Velocity of person = 52.50 kg·m/s - (4.10 kg × Velocity of skateboard)
Dividing throughout by 89.0 kg:
Velocity of person = (52.50 kg·m/s - (4.10 kg × Velocity of skateboard)) / 89.0 kg
Finally, we have an equation that relates the velocity of the person to the velocity of the skateboard. You can substitute in any value for the velocity of the skateboard to find the corresponding velocity of the person.
Similarly, you can solve for the velocity of the skateboard by rearranging the equation and substituting in values for the velocity of the person.
Note: The actual numerical values for the velocities cannot be determined without knowing the velocity of the skateboard.