A 970kg car is at the top of a 38m -long, 2.5 ∘ incline. Its parking brake fails and it starts rolling down the hill. Halfway down, it strikes and sticks to a 1280kg parked car.
Ignoring friction, what's the speed of the joined cars at the bottom of the incline?
What the first car's speed would have been at the bottom had it not struck the second car.
homework
38m*sin2.5°=1.66m
1.66/2=.829m <- 'halfway down'
v=Sqrt(2*9.81*.829)=4.03m/s
970*4.03=(970+1280)*V V=1.733m/s
.5(2250)(1.73)^2+2250*9.8*.829=21646.5 J
21646.5=.5(2250)(V)^2 V=4.39m/s
The speed of the joined cars is 4.39m/s
Sqrt(2*9.8*1.66)=5.7m/s
The first cars speed would have been 5.7m/s
I hope that wasn't too confusing.
To solve these problems, we can use the principle of conservation of mechanical energy.
First, let's find the speed of the joined cars at the bottom of the incline.
1. Calculate the potential energy at the top of the incline for the first car:
Potential Energy (PE) = mass (m1) × gravity (g) × height (h1)
PE1 = 970 kg × 9.8 m/s^2 × 38 m
2. Calculate the potential energy at the top of the incline for the second car:
PE2 = 1280 kg × 9.8 m/s^2 × 19 m (half the length of the incline since the collision happens halfway down)
3. Calculate the total potential energy at the top of the incline:
Total PE = PE1 + PE2
4. Using the principle of conservation of mechanical energy, the total potential energy at the top of the incline will be converted to the total kinetic energy at the bottom of the incline:
Total KE = Total PE
5. Calculate the total kinetic energy at the bottom of the incline:
Total KE = (1/2) × total mass (m1 + m2) × velocity^2
6. Rearrange the equation and solve for velocity:
velocity = sqrt((2 × Total KE) / (m1 + m2))
Now, let's find the speed of the first car had it not struck the second car:
1. Calculate the total potential energy at the top of the incline for the first car (same as step 1 above).
PE1 = 970 kg × 9.8 m/s^2 × 38 m
2. Using the principle of conservation of mechanical energy, the total potential energy at the top of the incline will be converted to the total kinetic energy at the bottom of the incline:
Total KE = PE1
3. Calculate the kinetic energy at the bottom of the incline for the first car:
KE1 = (1/2) × m1 × velocity^2
4. Rearrange the equation and solve for velocity:
velocity = sqrt((2 × Total KE) / m1)
By following these steps, you should be able to calculate the speed of the joined cars at the bottom of the incline and the speed of the first car had it not struck the second car.