62kg person in an elevator is moving up at a constant speed of 4.0m/s for 5.0s
a) calculate the work done by the normal force on the person.
b) calculate the work done by the force of gravity on the person .
c) How would your answer change if the elevator were moving down at 4.0m/s for 5.0s ?!
I am getting 6082.2 instead of 1200J for both help please
constant speed means no acceleration
F = m g = 608 N
W = force * distance = 608*4*5
= 12,164 Joules
same but force opposite to motion for gravity -12,164
signs reverse if going down
To calculate the work done, we can use the formula:
Work = force x distance x cosine(theta)
Where force is the magnitude of the force applied, distance is the displacement of the object, and theta is the angle between the force and displacement vectors.
a) To find the work done by the normal force on the person, we need to determine the force and distance.
The normal force is equal to the weight of the person, given by W = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
W = (62 kg) * (9.8 m/s^2) = 607.6 N (rounded to one decimal place)
Since the elevator is moving up at a constant speed, the displacement is simply the vertical distance traveled, which can be calculated using the formula:
Displacement = speed x time = (4.0 m/s) * (5.0 s) = 20.0 m
Now we can calculate the work done by the normal force using the formula:
Work = force x distance x cosine(theta) = 607.6 N * 20.0 m * cos(0) = 12,152 J (rounded to the nearest whole number)
b) To find the work done by the force of gravity on the person, we need to calculate the force and distance.
The force of gravity is equal to the weight of the person, which we have already calculated to be 607.6 N.
Since the elevator is moving up, the force of gravity and the displacement have opposite directions. Thus, the angle between the force and displacement vectors is 180 degrees.
Using the formula for work:
Work = force x distance x cosine(theta) = 607.6 N * 20.0 m * cos(180) = -12,152 J (rounded to the nearest whole number). Note the negative sign indicates the opposite direction.
c) If the elevator were moving down at 4.0 m/s for 5.0 s, the calculations for the work done by the normal force and the force of gravity would remain the same.
The work done by the normal force would still be 12,152 J, as the displacement is the same and the angle between the force and displacement vectors remains 0 degrees.
The work done by the force of gravity would still be -12,152 J, as the displacement is still the same, but the angle between the force and displacement vectors changes to 180 degrees.
Therefore, in both cases, the correct answer for both parts (a) and (b) is 12,152 J.
Please double-check your calculations and make sure to round the values appropriately.
To calculate the work done by the normal force on the person, you can use the formula:
Work = Force x Distance x cosθ
Where:
- Force is the magnitude of the normal force exerted by the elevator on the person.
- Distance is the vertical displacement of the person in the elevator.
- θ is the angle between the direction of the normal force and the direction of displacement (which is 0 degrees since the normal force and displacement are in the same direction).
a) Since the elevator is moving vertically upwards with a constant speed, the net force on the person is zero (since the acceleration is zero). Therefore, the normal force and the force of gravity are equal in magnitude but opposite in direction.
To find the work done by the normal force, we need to calculate the distance the person moves upwards during the 5.0 seconds. The distance travelled by the person can be calculated using the equation:
Distance = Speed x Time
Distance = 4.0 m/s x 5.0 s = 20.0 m
Now, we can substitute the values into the work formula:
Work = Force x Distance x cosθ
Since the force and displacement are in the same direction (θ = 0 degrees), the cosine of 0 degrees is 1:
Work = Force x Distance x 1
Since the net force is zero, the normal force and the force of gravity are equal. The weight of the person can be calculated using the formula:
Weight = mass x acceleration due to gravity
Weight = 62 kg x 9.8 m/s^2 = 607.6 N
Therefore, the work done by the normal force is:
Work = 607.6 N x 20.0 m = 12,152 J
So, the correct answer for part a) is 12,152 J.
b) The work done by the force of gravity can be calculated using the same formula:
Work = Force x Distance x cosθ
In this case, the force of gravity is acting in the opposite direction to the displacement. So, the angle θ is 180 degrees. The cosine of 180 degrees is -1:
Work = Force x Distance x (-1)
Therefore, the work done by the force of gravity is:
Work = 607.6 N x 20.0 m x (-1) = -12,152 J
So, the correct answer for part b) is -12,152 J.
c) If the elevator were moving downwards at 4.0 m/s for 5.0 s, the direction of the displacement would be opposite to the force of gravity. Thus, θ would be 180 degrees. In this case, using the same calculations as in part b), the work done by the force of gravity would be -12,152 J, and the work done by the normal force would be +12,152 J. The negative sign denotes the direction of work done in the opposite direction to the displacement. So, the correct answers for part c) are -12,152 J for the work done by the force of gravity and +12,152 J for the work done by the normal force.
Oh ho ho, let's calculate that work, my enlightened friend!
a) To calculate the work done by the normal force, we first need to find the net force acting on the person. Since the person is moving at a constant speed, the net force is zero. Therefore, the work done by the normal force is also zero. So no work done by the normal force, sorry to burst your bubble!
b) Now, let's calculate the work done by the force of gravity. The formula to calculate work is given as force multiplied by displacement. In this case, the force of gravity is equal to the weight of the person, which is mass multiplied by acceleration due to gravity (62 kg * 9.8 m/s^2). The displacement can be calculated by multiplying the speed by the time (4.0 m/s * 5.0 s). So the work done by the force of gravity is (62 kg * 9.8 m/s^2) * (4.0 m/s * 5.0 s). That's equal to 1204 J, my friend! So close, but not quite there with 1200 J.
c) Ah, a twist in the tale! If the elevator were moving down at 4.0 m/s for 5.0 s, the calculations would be a bit different. The work done by the normal force would still be zero because, just like before, the net force would be zero since the person is moving at a constant speed. However, the work done by the force of gravity would change because the displacement is now negative (-4.0 m/s * 5.0 s). So the work done by the force of gravity would be (62 kg * 9.8 m/s^2) * (-4.0 m/s * 5.0 s), which equals -1204 J. Ah, the negative sign means that the work done by gravity is in the opposite direction of the displacement.
So, my friend, I hope this clears things up for you. Be sure to check your calculations again, and remember, when it comes to physics, even a little clowning around can help you solve those pesky questions!