A 6.0 kh block, sliding to the east across a horizontal, frictionless surface with a momentum of 30 kg*m/s^, strikes an obstacle. The obstacle exerts an impluse of 10 N*s to the west on the book. The speed of the block after the collision is...
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Given
m = 6 kg
p = 30 kg*m/s
J = 10 n*s
J = Fnet t
I know you cant use the p = mv since this states impluse.
To find the speed of the block after the collision, we can use the principle of conservation of momentum.
The initial momentum of the block is given as 30 kg*m/s to the east. The impulse exerted by the obstacle is 10 N*s to the west.
According to the principle of conservation of momentum, the initial momentum of the block is equal to the final momentum of the block.
Therefore, 30 kg*m/s (initial momentum) = final momentum
To solve for the final momentum, we need to consider the direction of the impulse.
Impulse = change in momentum
The impulse is given as 10 N*s to the west, which means the momentum of the block will change by 10 kg*m/s to the west.
So, final momentum = initial momentum + change in momentum
= 30 kg*m/s + (-10 kg*m/s)
= 20 kg*m/s
Now, we can calculate the final speed of the block using the momentum formula:
Final momentum = mass * final velocity
where mass of the block is 6.0 kg.
20 kg*m/s = 6.0 kg * final velocity
Simplifying the equation, we have:
final velocity = 20 kg*m/s / 6.0 kg
≈ 3.33 m/s (rounded to two decimal places)
Therefore, the speed of the block after the collision is approximately 3.33 m/s.
To find the speed of the block after the collision, we need to use the principles of conservation of momentum and impulse.
Momentum is the product of mass and velocity, given by the equation:
momentum = mass * velocity
In this case, the initial momentum of the block before the collision is given as 30 kg*m/s to the east.
Using the principle of conservation of momentum, we can state that the total momentum before and after the collision should be the same, since there is no external net force acting on the system.
Before the collision: Momentum_before = mass * initial_velocity
After the collision: Momentum_after = mass * final_velocity
Given that the initial momentum is 30 kg*m/s, and the mass is 6.0 kg, we can plug these values into the equation and solve for the final velocity.
30 kg*m/s = 6.0 kg * final_velocity
Dividing both sides of the equation by 6.0 kg, we get:
final_velocity = 30 kg*m/s / 6.0 kg
final_velocity = 5.0 m/s
Therefore, the speed of the block after the collision is 5.0 m/s.