A camper does 7.4 x 102 J of work in lifting a pail filled with water 3.4 m vertically up a well at a constant speed.
a)What force is exerted by the camper on the pail of water?
b)What is the mass of water in the pail?
Work = force times distance
7.4 x 10^2 J = force x 3.4
divide by 3.4 to get the force in newtons.
Force = mass times gravity g= 9.8 m/sec^2
Divide your answer in part a by 9.8 to get the mass.
a) Well, let me calculate the force first. So, we know that work is equal to force multiplied by distance. In this case, the work done by the camper is 7.4x10² J and the distance is 3.4 m. So, force must be the work divided by the distance. Therefore, the force exerted by the camper on the pail of water is approximately 2.18x10² N.
b) Now, to find the mass of water in the pail, we can use Newton's second law, which states that force is equal to mass multiplied by acceleration. In this situation, the force is 2.18x10² N, and the acceleration of the water as it's being lifted is just the acceleration due to gravity, approximately 9.8 m/s². Therefore, the mass of water in the pail is approximately 2.22x10¹ kg.
But hey, be careful not to spill the beans... or in this case, the water!
a) To determine the force exerted by the camper on the pail of water, we can use the equation:
Work = Force x Distance
Given: Work = 7.4 x 10^2 J, Distance = 3.4 m
Substituting these values into the equation, we get:
7.4 x 10^2 J = Force x 3.4 m
To find the force, divide both sides of the equation by 3.4 m:
Force = 7.4 x 10^2 J / 3.4 m
Calculating this, we get:
Force ≈ 217.65 N
Therefore, the force exerted by the camper on the pail of water is approximately 217.65 N.
b) To find the mass of water in the pail, we can use the equation:
Force = mass x acceleration
Acceleration due to gravity, denoted by 'g', is 9.8 m/s².
Rearranging the equation, we get:
mass = Force / acceleration
Substituting the given values, we have:
mass = 217.65 N / 9.8 m/s²
Calculating this, we get:
mass ≈ 22.2 kg
Therefore, the mass of water in the pail is approximately 22.2 kg.
To answer these questions, we need to understand the concept of work, force, and gravitational potential energy.
a) Force exerted by the camper on the pail of water:
The work done by the camper in lifting the pail of water is equal to the force applied multiplied by the distance it is lifted. Mathematically, work (W) is given by the equation: W = F × d, where F represents the force and d is the distance. In this case, we are given the work (W) as 7.4 × 10^2 J (joules) and the distance (d) as 3.4 m (meters).
Therefore, we can rearrange the equation to solve for the force (F):
F = W / d
Now, substituting the given values:
F = 7.4 × 10^2 J / 3.4 m
F ≈ 217.65 N (approximately)
So, the force exerted by the camper on the pail of water is approximately 217.65 Newtons.
b) Mass of water in the pail:
To determine the mass of water in the pail, we need to use the concept of gravitational potential energy. Gravitational potential energy (PE) is the energy associated with an object due to its position relative to a gravitational field.
Mathematically, gravitational potential energy (PE) is given by: PE = m × g × h, where m represents the mass, g is the acceleration due to gravity (which is approximately 9.8 m/s² on Earth), and h represents the height or vertical distance.
In this case, the work done by the camper lifting the pail of water is equal to the change in gravitational potential energy of the water:
W = PE = m × g × h
Given that the work done (W) is 7.4 × 10^2 J and the height (h) is 3.4 m, we can rearrange the equation to solve for the mass (m):
m = W / (g × h)
Substituting the given values and the acceleration due to gravity (g) of 9.8 m/s²:
m = 7.4 × 10^2 J / (9.8 m/s² × 3.4 m)
m ≈ 22.22 kg (approximately)
Therefore, the mass of water in the pail is approximately 22.22 kilograms.