An 800kg car moving at 80kmh^-1 collides with a 1200kg car moving at 40kmh^-1 in the same direction. If the car sticks together, calculate their common speed
conserve momentum.
800*80 + 1200*40 = (800+1200)v
60 kmph
To calculate the common speed of the two cars after they stick together, we can use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity.
The initial momentum of the first car is equal to the mass of the first car multiplied by its initial velocity:
Momentum1 = (mass1)(velocity1)
The initial momentum of the second car is equal to the mass of the second car multiplied by its initial velocity:
Momentum2 = (mass2)(velocity2)
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
Momentum1 + Momentum2 = Total Momentum
After the collision, the two cars stick together and move with a common speed. Let's call this common speed "v".
So, the total momentum after the collision is given by:
Total Momentum = (mass1 + mass2) * v
Now, we can set up an equation based on the conservation of momentum principle:
(mass1)(velocity1) + (mass2)(velocity2) = (mass1 + mass2) * v
Substituting the given values:
(800 kg)(80 km/h) + (1200 kg)(40 km/h) = (800 kg + 1200 kg) * v
Converting the velocities to meters per second (m/s) by dividing them by 3.6:
(800 kg)(80 km/h ÷ 3.6) + (1200 kg)(40 km/h ÷ 3.6) = (800 kg + 1200 kg) * v
(800 kg)(22.22 m/s) + (1200 kg)(11.11 m/s) = (800 kg + 1200 kg) * v
17776 kg·m/s + 13332 kg·m/s = 2000 kg * v
31108 kg·m/s = 2000 kg * v
Dividing both sides by 2000 kg to solve for v:
v = 31.11 m/s
Therefore, the common speed of the cars after they stick together is 31.11 m/s.
To calculate the common speed of the cars after the collision, we first need to calculate the total momentum of the system before the collision and after the collision.
Momentum is defined as the product of mass and velocity. The formula for momentum is:
Momentum (p) = mass (m) × velocity (v)
Before the collision, the total momentum of the system is the sum of the individual momenta of the cars.
The momentum of the 800 kg car moving at 80 km/h is:
p1 = m1 × v1
= 800 kg × 80 km/h
= 64000 kg·km/h
The momentum of the 1200 kg car moving at 40 km/h is:
p2 = m2 × v2
= 1200 kg × 40 km/h
= 48000 kg·km/h
The total momentum of the system before the collision is:
p_total_before = p1 + p2
= 64000 kg·km/h + 48000 kg·km/h
= 112000 kg·km/h
After the collision, the two cars stick together, so their combined mass is the sum of their individual masses, and the common speed is the same for both cars.
The combined mass of the cars is:
m_total = m1 + m2
= 800 kg + 1200 kg
= 2000 kg
Let's assume the common speed after the collision is v_common.
The total momentum of the system after the collision is:
p_total_after = m_total × v_common
Since momentum is conserved in a collision, the total momentum before and after the collision remains the same:
p_total_before = p_total_after
Therefore, we can set up the following equation:
112000 kg·km/h = 2000 kg × v_common
To calculate the common speed (v_common), we need to convert the units to a common unit (e.g., m/s):
112000 kg·km/h = 2000 kg × (v_common m/s)
To convert km/h to m/s, divide by 3.6:
(112000 kg·km/h) / 3.6 = 2000 kg × v_common
Now, solve for v_common:
v_common = (112000 kg·km/h) / (2000 kg)
= 56 m/s
Therefore, the common speed of the two cars after the collision is 56 m/s.