a 4-kg box is pushed across a level floor with a force of 60n for a displacemen of 20m then lifted to a height of 3 m. what is total work done on the box?

To calculate the total work done on the box, we need to calculate the work done while pushing the box and the work done while lifting the box.

1. Work done while pushing the box:
The work done while pushing the box is given by the formula:
Work = Force x Displacement x cos(theta)
where,
Force = 60N (given)
Displacement = 20m (given)
cos(theta) = cos(0 degrees) = 1 (since the force is applied horizontally, the angle between the force and displacement is 0 degrees)

Plugging in the values:
Work_pushing = 60N x 20m x 1 = 1200 Joules

2. Work done while lifting the box:
The work done while lifting the box against gravity is given by the formula:
Work = Force x Displacement x cos(theta)
where,
Force = Weight of the box
Displacement = 3m (given)
cos(theta) = cos(180 degrees) = -1 (since the force is applied vertically opposite to the displacement)

Weight of the box = mass x acceleration due to gravity
mass = 4kg (given)
acceleration due to gravity = 9.8 m/s^2

Weight of the box = 4kg x 9.8 m/s^2 = 39.2N

Plugging in the values:
Work_lifting = 39.2N x 3m x -1 = -117.6 Joules (since cos(180 degrees) = -1)

3. Total work done on the box:
Total work = Work_pushing + Work_lifting
Total work = 1200 Joules + (-117.6 Joules) = 1082.4 Joules

Therefore, the total work done on the box is 1082.4 Joules.

To calculate the total work done on the box, we need to consider both the work done while pushing the box and the work done while lifting the box.

1. Work done while pushing the box:
The work done while pushing the box is given by the equation: work = force * displacement * cos(theta).
In this case, the force applied to the box is 60N, and the displacement is 20m.
Since the box is being pushed along a level floor, theta (the angle between the direction of the force and the direction of displacement) is 0 degrees. Therefore, cos(0) = 1.
So, the work done while pushing the box is: work = 60N * 20m * cos(0) = 60N * 20m * 1 = 1200 Joules (J).

2. Work done while lifting the box:
The work done while lifting the box is given by the equation: work = force * displacement * cos(theta).
In this case, the force applied to lift the box is equal to the weight of the box.
The weight of the box can be calculated using the formula: weight = mass * acceleration due to gravity.
The mass of the box is given as 4kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
So, the weight of the box is: weight = 4kg * 9.8 m/s^2 = 39.2N.
Now, the displacement while lifting the box is given as a height of 3m.
Since the force and displacement are in the same direction (upwards), theta is also 0 degrees (cos(0) = 1).
Therefore, the work done while lifting the box is: work = 39.2N * 3m * cos(0) = 39.2N * 3m * 1 = 117.6 Joules (J).

To calculate the total work done on the box, we add up the work done while pushing and lifting:
Total work = Work done while pushing + Work done while lifting
Total work = 1200J + 117.6J = 1317.6 Joules (J).

So, the total work done on the box is 1317.6 Joules (J).

(Work against friction) + (Work against gravity)

(60 N x 20 m) + (M*g)* 2 m

You know what M and g are.

Add the two terms