How much work is done when a mass of 3 kg (weighing 30 N)
is lifted vertically through 6 m?.
A hiker climbs a hill 300 m high. If she has a mass of 50 kg
calculate the work she does in lifting her body to the top of the
hill.
work = force * distance = 30 N * 6 m
... answer is in Joules
work = m g h = 50 * 9.8 * 300
Thank you
To calculate the work done in lifting an object vertically, we can use the formula:
Work = force * distance
1. For the first question, the mass of the object is 3 kg, and its weight is given as 30 N. Since weight is the force exerted by gravity, we can use weight as the force.
Work = force * distance
= 30 N * 6 m
= 180 Joules
Therefore, the work done to lift the 3 kg mass vertically through 6 m is 180 Joules.
2. For the second question, the mass of the hiker is 50 kg. we need to calculate the force to lift her body to the top of the hill. The force exerted by gravity is given by her weight.
Weight = mass * gravity
= 50 kg * 9.8 m/s^2
= 490 N
Now, we can calculate the work done by multiplying the force by the distance.
Work = force * distance
= 490 N * 300 m
= 147,000 Joules
Therefore, the work done in lifting the hiker's body to the top of the hill is 147,000 Joules.
To find the work done in both scenarios, we need to use the formula:
Work = Force x Distance x Cosine(theta)
Where:
- Work is the amount of work done, measured in joules (J).
- Force is the force applied, measured in newtons (N).
- Distance is the distance the object is moved, measured in meters (m).
- Theta (θ) is the angle between the force and the direction of displacement.
In the first scenario, a mass of 3 kg is lifted vertically through 6 m, and the weight is given as 30 N. Since the object is lifted vertically, the angle between the force and the direction of displacement is 0 degrees (cosine(0) = 1).
So, for the first scenario:
- Force = 30 N
- Distance = 6 m
- Theta = 0 degrees (which means cosine(0) = 1)
Plugging these values into the formula, we get:
Work = 30 N x 6 m x 1
Work = 180 J
Therefore, in the first scenario, when a mass of 3 kg is lifted vertically through 6 m, the amount of work done is 180 joules.
In the second scenario, a hiker climbs a hill 300 m high, and her mass is given as 50 kg. The force applied is equal to her weight, which can be calculated using the formula:
Force = Mass x Gravity
Where:
- Mass is the mass of the object, measured in kilograms (kg).
- Gravity is the acceleration due to gravity, approximately equal to 9.8 m/s^2.
So, for the second scenario:
- Mass = 50 kg
- Gravity = 9.8 m/s^2 (approx.)
Plugging these values into the formula, we get:
Force = 50 kg x 9.8 m/s^2
Force = 490 N
The distance is given as 300 m, and since the hiker is climbing vertically, again the angle between the force and the direction of displacement is 0 degrees (cosine(0) = 1).
So, for the second scenario:
- Force = 490 N
- Distance = 300 m
- Theta = 0 degrees (which means cosine(0) = 1)
Plugging these values into the formula, we get:
Work = 490 N x 300 m x 1
Work = 147,000 J
Therefore, in the second scenario, when the hiker climbs a hill 300 m high, the amount of work done is 147,000 joules.