A boy and his skateboard have a combined mass of 64 kg. If he is moving with a speed of
3.2 m/s, and collides with a stationary skateboarder whose mass (including his skateboard) is
96 kg, with what speed will the two skateboarders move immediately after the collision?
p=mv
M1V1=M2V2
(64kg)(3.2m/s)=(96+64)(V2)
(64kg)(3.2m/s)/160kg=V2
1.28m/s= V2
Why did the skateboarders decide to collide? They must have thought it was a good way to bond! Anyway, let's calculate the speed after the collision using the law of conservation of momentum.
The momentum before the collision is given by:
momentum_before = (mass_boy + mass_skateboard) * velocity_boy
momentum_before = (64 kg + 96 kg) * 3.2 m/s
momentum_before = 320 kg * 3.2 m/s
momentum_before = 1024 kg*m/s
Now, let's find the momentum after the collision. Since momentum is conserved, we can set the sum of the momenta before equal to the sum of the momenta after the collision.
momentum_before = momentum_after
(64 kg + 96 kg) * 3.2 m/s = (mass_boy + mass_skateboard) * final_velocity
(160 kg) * 3.2 m/s = (160 kg + 96 kg) * final_velocity
512 kg*m/s = 256 kg * final_velocity
final_velocity = 512 kg*m/s / 256 kg
final_velocity = 2 m/s
So, after the collision, the two skateboarders will move together at a speed of 2 m/s. Now they can continue their wild skateboarding adventures together!
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) is given by:
p = m * v
Where:
p = momentum
m = mass
v = velocity
Let's assume the velocity of the two skateboarders immediately after the collision is v_f. We can express the initial momentum and the final momentum as follows:
Initial momentum before collision = momentum of the boy + momentum of the stationary skateboarder
Final momentum after collision = momentum of the two skateboarders moving together
According to the principle of conservation of momentum, the initial momentum before the collision is equal to the final momentum after the collision:
(mass of boy * velocity of boy) + (mass of stationary skateboarder * velocity of stationary skateboarder) = (combined mass of boy and skateboard * velocity after collision)
Let's plug in the given values into the equation:
(64 kg * 3.2 m/s) + (96 kg * 0) = (160 kg * v_f)
(204.8 kg * m/s) = (160 kg * v_f)
Now, let's calculate the velocity after the collision (v_f):
v_f = (204.8 kg * m/s) / (160 kg)
v_f = 1.28 m/s
Therefore, the two skateboarders will move together with a speed of 1.28 m/s immediately after the collision.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum is given by the product of mass and velocity. Thus, the momentum before the collision (P1) can be calculated as:
P1 = m1 * v1 + m2 * v2
where
m1 = mass of the boy
v1 = velocity of the boy before the collision
m2 = mass of the skateboarder
v2 = velocity of the skateboarder before the collision
Given:
m1 = mass of the boy = 64 kg
v1 = velocity of the boy = 3.2 m/s
m2 = mass of the skateboarder = 96 kg
v2 = velocity of the skateboarder = 0 m/s (since he is stationary)
We can substitute these values into the equation to find the total momentum before the collision:
P1 = (64 kg) * (3.2 m/s) + (96 kg) * (0 m/s)
P1 = 204.8 kg·m/s
After the collision, the two skateboarders will move together with a common velocity, which we can call v_f (final velocity). To find this velocity, we can equate the total momentum before the collision with the total momentum after the collision:
P1 = P_f
where
P_f = total momentum after the collision
The total momentum after the collision (P_f) can be calculated as:
P_f = (m1 + m2) * v_f
Substituting the given values:
P_f = (64 kg + 96 kg) * v_f
P_f = 160 kg * v_f
Setting P_f equal to P1:
P1 = P_f
204.8 kg·m/s = 160 kg * v_f
Now, we can solve for v_f by dividing both sides by 160 kg:
v_f = 204.8 kg·m/s / 160 kg
v_f = 1.28 m/s
Therefore, the two skateboarders will move immediately after the collision with a speed of 1.28 m/s.