# A 500gcart is released from rest 1.00mfrom the bottom of frictionless 30 deg ramp.?

The cart rolls down the ramp and bounces off a rubber block at the bottom. The figure shows the force during the collision. The cart rolls down the ramp and bounces off a rubber block at the bottom. The figure shows the force during the collision. Max at 200 N during time interval of 26.7 ms

A 500gcart is released from rest 1.00 m from the bottom of frictionless 30 deg ramp.?
The cart rolls down the ramp and bounces off a rubber block at the bottom. The figure shows the force during the collision. The cart rolls down the ramp and bounces off a rubber block at the bottom. The figure shows the force during the collision. Max at 200 N during time interval of 26.7 ms
After the cart bounces, how far does it roll back up the ramp?

When the cart initially this the rubber block, the force exerted by the rubber (elastic) block = 0 N
The Maximum force = 200 N
Average force = ½ * (0 + 200) = 100 N
Force * time = mass * ∆ velocity
100 * 26.7 * 10^-3 = 0.500 * ∆ velocity
∆ velocity = 100 * 0.0267 ÷ 0.500 = 5.34 m/s

When the car bounces off a rubber block at the bottom, the new velocity of car will equal velocity of cart at time of collision – 5.34 m/s

Force parallel causes the acceleration
Acceleration = Force parallel ÷ mass
Force parallel = mass * g * sin θ
Acceleration = mass * g * sin θ ÷ mass = g * sin θ
Acceleration = 9.8 * sin 30° = 4.9 m/s^2

Final velocity^2 – Initial velocity^2 =2 * a * d
Final velocity^2 – 0^2 = 2 * 4.9 * 1.00 = 9.8
Final velocity = 9.8^0.5 = 3.13 m/s = velocity of cart at time of collision

New velocity = 3.13 – 5.34 = -2.21 m/s
Negative means the direction of the new velocity is opposite the direction of velocity of cart at time of collision.

Negative means the cart is rolling UP the incline with an initial velocity of 2.21 m/s

As the cart rolls up the incline, acceleration = -4.9 m/s^2
Final velocity^2 – Initial velocity^2 =2 * a * d
Final velocity = 0
Initial velocity = 2.21
-2.21^2 = 2 * -4.9 * d
d = 0.5 m