A 0.2kg toy car rolls down a ramp with a height of 0.7m. What is the speed of the car at the bottom of the ramp. At the bottom it hits a stationary car with a mass of .4 kg. The two cars have velcro bumpers and stick together. At what speed do the two cars move after the collision?
V = √(2 g h)
momentum is conserved
... .2 * V = (.2 + .4) v
Thank you
To find the speed of the toy car at the bottom of the ramp, we can use the principle of conservation of energy. The potential energy of the car at the top of the ramp gets converted into its kinetic energy at the bottom of the ramp.
First, let's calculate the potential energy (PE) of the toy car at the top of the ramp using the formula PE = mgh, where m is the mass of the car (0.2 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the ramp (0.7 m).
PE = 0.2 kg * 9.8 m/s^2 * 0.7 m
PE = 1.372 J
Next, let's calculate the kinetic energy (KE) of the car at the bottom of the ramp using the formula KE = 0.5 * mv^2, where m is the mass of the car (0.2 kg) and v is the velocity/speed of the car.
KE = 0.5 * 0.2 kg * v^2
Since the potential energy is converted into kinetic energy, we can equate the two:
PE = KE
1.372 J = 0.5 * 0.2 kg * v^2
Now, let's solve for v:
v^2 = (2 * 1.372 J) / 0.2 kg
v^2 = 13.72 J / 0.2 kg
v^2 = 68.6 m^2/s^2
Taking the square root of both sides, we find:
v = √(68.6 m^2/s^2)
v ≈ 8.28 m/s
Therefore, the speed of the toy car at the bottom of the ramp is approximately 8.28 m/s.
Now, let's move on to the second part of the question regarding the collision between the toy car and the stationary car. Since the two cars have velcro bumpers and stick together, the collision is inelastic. In an inelastic collision, the kinetic energy is not conserved, but the momentum is conserved.
Let's use the principle of conservation of momentum to find the speed after the collision. The initial momentum (p_initial) is given by the mass (m) of the toy car multiplied by its velocity (v):
p_initial = m * v
The final momentum (p_final) is the sum of the initial momentum of the two cars, since they stick together:
p_final = (m_toy car * v_toy car) + (m_stationary car * 0), since the stationary car has zero velocity initially
Since momentum is conserved, we can set p_initial equal to p_final:
m_toy car * v = (m_toy car + m_stationary car) * v_final
Now, let's solve for v_final:
v_final = (m_toy car * v) / (m_toy car + m_stationary car)
v_final = (0.2 kg * 8.28 m/s) / (0.2 kg + 0.4 kg)
v_final = (1.656 kg·m/s) / (0.6 kg)
v_final ≈ 2.76 m/s
Therefore, the two cars move together at a speed of approximately 2.76 m/s after the collision.