3 kg block (block A) is released from rest at the top of a 20 m long frictionless ramp that is 5 m high. At the same time, an identical block (block B) is released next to the ramp so that it drops straight down the same 5 m. Find the values for each of the following for the blocks just before they reach ground level.
(a) gravitational potential energy
Block A
J
Block B
J
(b) kinetic energy
Block A
J
Block B
J
(c) speed
Block A
m/s
Block B
m/s
(d) momentum
Block A
kg·m/s
Block B
kg·m/s
To solve this problem, we will need to apply the concepts of conservation of energy and conservation of momentum.
(a) Gravitational Potential Energy:
The gravitational potential energy of an object is given by the equation:
Potential Energy = mass x gravity x height
For Block A:
Mass of Block A = 3 kg
Height = 5 m
Gravity = 9.8 m/s^2
Potential Energy of Block A = 3 kg x 9.8 m/s^2 x 5 m = 147 J
For Block B:
Mass of Block B = 3 kg
Height = 5 m
Gravity = 9.8 m/s^2
Potential Energy of Block B = 3 kg x 9.8 m/s^2 x 5 m = 147 J
(b) Kinetic Energy:
The kinetic energy of an object is given by the equation:
Kinetic Energy = (1/2) x mass x velocity^2
At the moment just before reaching the ground, both blocks will have the same velocity since they are at the same height and have traveled the same vertical distance.
For Block A:
Mass of Block A = 3 kg
Velocity of Block A = unknown (let's call it V)
Kinetic Energy of Block A = (1/2) x 3 kg x V^2 = 1.5V^2 J
For Block B:
Mass of Block B = 3 kg
Velocity of Block B = unknown (let's call it V)
Kinetic Energy of Block B = (1/2) x 3 kg x V^2 = 1.5V^2 J
(c) Speed:
Since both blocks A and B have traveled the same vertical distance of 5 m, they will have the same speed just before reaching the ground.
For Block A, the speed is equal to the velocity, so it is V m/s.
For Block B, the speed is equal to the velocity, so it is also V m/s.
(d) Momentum:
Momentum is the product of an object's mass and its velocity.
For Block A:
Mass of Block A = 3 kg
Velocity of Block A = V m/s
Momentum of Block A = 3 kg x V m/s = 3V kg·m/s
For Block B:
Mass of Block B = 3 kg
Velocity of Block B = V m/s
Momentum of Block B = 3 kg x V m/s = 3V kg·m/s
So, the answers are:
(a) Gravitational potential energy:
Block A: 147 J
Block B: 147 J
(b) Kinetic energy:
Block A: 1.5V^2 J
Block B: 1.5V^2 J
(c) Speed:
Block A: V m/s
Block B: V m/s
(d) Momentum:
Block A: 3V kg·m/s
Block B: 3V kg·m/s