How much impulse stops a 46-kg carton sliding at 3.0m/s when it meets a rough surface?
To calculate the impulse required to stop the carton, we can use the equation:
Impulse = mass × change in velocity
Given:
Mass (m) = 46 kg
Initial velocity (u) = 3.0 m/s (since the carton is sliding)
Final velocity (v) = 0 m/s (since the carton comes to a stop)
Change in velocity (Δv) = v - u = 0 - 3.0 = -3.0 m/s (negative because the carton is slowing down)
Now, we can calculate the impulse using the equation:
Impulse = mass × change in velocity
Impulse = 46 kg × (-3.0 m/s)
Impulse = -138 kg·m/s
Therefore, the impulse required to stop the carton is -138 kg·m/s. The negative sign indicates that the impulse is in the opposite direction of the initial motion of the carton.
To calculate the impulse, we need to use the formula: impulse = change in momentum.
The momentum of an object can be calculated using the formula: momentum = mass * velocity.
Given that the carton has a mass of 46 kg and is sliding at a velocity of 3.0 m/s, we can calculate its initial momentum.
Initial momentum = mass * initial velocity
= 46 kg * 3.0 m/s
Now, at the moment the carton meets the rough surface, it comes to rest. Therefore, its final velocity is 0 m/s.
Final momentum = mass * final velocity
= 46 kg * 0 m/s
= 0 kg·m/s
The change in momentum is then the difference between the initial and final momentum.
Change in momentum = Final momentum - Initial momentum
= 0 kg·m/s - (46 kg * 3.0 m/s)
Now, let's calculate the impulse by using the formula:
impulse = change in momentum
Substituting the values, we get:
impulse = 0 kg·m/s - (46 kg * 3.0 m/s)
To get the final answer, we need an actual value for one of the speeds of the rough surface, since "meeting" is not well defined.
F dt = change in momentum = 46(0-3)
= -138 kg m/s