A 5.o kg box is lifted to a height of 10 meters at a constant speed.
a)How much power is required to complete this task in 10 seconds?
b)Calculate the velocity of the box just as it hits the ground?
i have the answers but i need a second opinion
a)50 watts
b)?
a) M*g*H/t = 5*9.8*10/10 = 49 W
b) If it is released from 10 meters up,
V = sqrt(2gH) = 14.0 m/s
I used g = 9.8 m/s^2. Perhaps they told you to use 10 instead. It isn't that hard to remember the correct value.
To find the answers to these questions, we'll need to use some physics equations. Let's break it down step by step:
a) How much power is required to complete this task in 10 seconds?
Power (P) is given by the formula:
P = Work / Time.
We need to calculate the work done first. The work done (W) is given by the formula:
W = force * distance.
In this case, the force is equal to the weight of the box, which is given by:
force = mass * gravity.
So, force = 5 kg * 9.8 m/s^2 (acceleration due to gravity) = 49 N.
The distance is given as 10 meters.
Therefore, the work done (W) = 49 N * 10 meters = 490 J (Joules).
Now, substitute the work and the time (10 seconds) into the power formula:
P = 490 J / 10 s = 49 watts.
So, the answer is 49 watts, not 50 watts as you mentioned.
b) To calculate the velocity of the box just as it hits the ground, we can use the equation of motion:
v^2 = u^2 + 2as.
In this case, the box is lifted to a height of 10 meters, so the displacement (s) is -10 meters (negative because the box is moving in the opposite direction of gravity).
The initial velocity (u) is 0, as the box starts from rest.
The acceleration (a) is given by:
a = gravitational acceleration = 9.8 m/s^2.
Now, we can substitute the values into the equation:
v^2 = 0^2 + 2 * 9.8 m/s^2 * (-10 m).
v^2 = 0 + (-196) m^2/s^2.
v^2 = -196 m^2/s^2.
Since velocity cannot be negative in this context, we disregard the negative sign.
Taking the square root of both sides, we find:
v = sqrt(196) m/s.
So, the velocity of the box just as it hits the ground is:
v = 14 m/s, not the available answer in your question.
Remember, it's essential to double-check the calculations to ensure accuracy.