# How much work would it take to push a # 5 kg # weight up a # 4 m # plane that is at an incline of # pi / 4 #?

The explanation below includes two possible approaches to this calculation. The answer (in some ways the least interesting bit!) is

The solution to this problem can be computed in at least two different ways.

In the second, the object's energy is changed by work; in this example, sliding the object up the ramp raises its height and, consequently, its gravitational potential energy.

Trigonometry and the definition of sine are used in the calculation of the height:

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To calculate the work done, you can use the formula: Work = Force × Distance × Cosine(angle). Given that the weight is 5 kg and the incline angle is π/4 radians (45 degrees), the force required can be calculated using the weight and the angle. The force required is equal to the weight times the sine of the angle. Then, you can calculate the work using the given distance and the calculated force.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A spring with a constant of #4 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3 kg# and speed of #1 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- An object with a mass of #12 kg# is moving at #9 m/s# over a surface with a kinetic friction coefficient of #1 #. How much power will it take to accelerate the object at #3 m/s^2?
- How much work would it take to push a # 1 kg # weight up a # 4 m # plane that is at an incline of # (5pi) / 12 #?
- A balanced lever has two weights on it, the first with mass #6 kg # and the second with mass #8 kg#. If the first weight is # 4 m# from the fulcrum, how far is the second weight from the fulcrum?
- How much work would it take to push a # 6 kg # weight up a # 2 m # plane that is at an incline of # pi / 4 #?

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