2. A 75.0-kg painter climbs a ladder that is 2.75 m long leaning against a vertical wall. The ladder makes a 30.0° angle with the wall.
(a) How much work does is done by gravity on the painter?
(b) Does the answer to part (a) depend on whether the painter climbs at constant speed or accelerates up the ladder?
a. work=force.distance where the dot means cosine of angle between them
work=mg*2.75 cosine30 that is the work done by the painter, the work done by gravity is the negative of that.
a painter climbs a ladder that is 2,75 m long leaning against a vertical wall.the ladder makes 30 degrees with the wall.how much work does gravity do on the painter
(a) Well, gravity always likes to give a helping hand (or force) when it comes to doing work. In this case, the work done by gravity on the painter can be calculated using the equation W = mgh, where m is the mass of the painter, g is the acceleration due to gravity, and h is the vertical height climbed by the painter. Since the ladder is at an angle, we need to calculate the vertical height climbed. Using a bit of trigonometry, we find that h = 2.75 m * sin(30°). So, the work done by gravity on the painter is W = 75.0 kg * 9.8 m/s^2 * 2.75 m * sin(30°).
(b) As for the question of whether the answer depends on the painter climbing at a constant speed or accelerating, well, it depends on whether gravity is feeling lazy or not. Just kidding! Actually, the work done by gravity does not depend on the speed at which the painter climbs the ladder. Regardless of whether the painter climbs at a constant speed or accelerates, gravity will always exert the same force and do the same amount of work. So, let gravity do its thing and pull that painter up without worrying about the speed!
To find the answer to part (a) of the question, we can use the concept of work done by gravity. Work done is calculated by multiplying the force applied by an object with the distance it moves in the direction of the force. In this case, the force applied by gravity is equal to the painter's weight.
To calculate the weight, we use the formula:
weight = mass x gravity
Given that the mass of the painter is 75.0 kg, and assuming the acceleration due to gravity is 9.8 m/s^2, we can calculate the weight as follows:
weight = 75.0 kg x 9.8 m/s^2 = 735 N
Now, to calculate the work done by gravity, we multiply the weight by the distance the painter moves in the direction of the force.
The distance the painter moves can be found using the ladder's length and angle with the wall. From the given information, we know that the ladder is 2.75 m long and makes a 30.0° angle with the wall.
To calculate the distance the painter moves vertically, we use the formula:
distance = ladder length x sin(angle)
distance = 2.75 m x sin(30.0°) = 2.75 m x 0.5 = 1.375 m
Now, we can calculate the work done by gravity using the formula:
work = force x distance
work = weight x distance
work = 735 N x 1.375 m = 1011.56 J
Therefore, the work done by gravity on the painter is approximately 1011.56 Joules.
Moving on to part (b) of the question, the answer does not depend on whether the painter climbs at a constant speed or accelerates. The work done by gravity is determined solely by the vertical distance the painter climbs and the force of gravity acting on the painter, which is the weight of the painter. The work done is independent of how quickly or slowly the painter climbs the ladder.