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? assume they are hopelessly entangled, but their wheels point in the same direction
mv=(m+M)u
u=mv/(m+M)
To determine the speed at which the two skateboarders move immediately after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
1. Calculate the initial momentum before the collision:
Momentum = Mass * Velocity
For the boy: Momentum_boy = Mass_boy * Velocity_boy
= 64 kg * 3.2 m/s
= 204.8 kg·m/s
For the stationary skateboarder: Momentum_skateboarder = Mass_skateboarder * Velocity_skateboarder
= 96 kg * 0 m/s (since he is stationary)
= 0 kg·m/s
Total initial momentum: Momentum_initial = Momentum_boy + Momentum_skateboarder
= 204.8 kg·m/s + 0 kg·m/s
= 204.8 kg·m/s
2. Since the skateboarders are hopelessly entangled after the collision, their masses combine, and they move together as one system. Let's assume their final combined mass is M_f and their final velocity is v_f.
Total final momentum: Momentum_final = M_f * v_f
3. According to the law of conservation of momentum, the total initial momentum should be equal to the total final momentum.
Momentum_initial = Momentum_final
204.8 kg·m/s = M_f * v_f
4. We know that the final combined mass of the skateboarders is 64 kg + 96 kg = 160 kg.
Substituting the values into the equation:
204.8 kg·m/s = 160 kg * v_f
5. Solve for v_f:
v_f = 204.8 kg·m/s / 160 kg
= 1.28 m/s
Therefore, the skateboarders will move with a speed of 1.28 m/s immediately after the collision.