A person pushes a block up a frictionless incline at a constant velocity. The incline is 35o, and the mass of the block is 28 kg. If he only exerts a horizontal force, how much work does he do if the block travels 7 m along the incline?
If he moves the block at constant velocity, and the incline is frictionless, the work he performs equals the potential energy increase achieved.
W = M*g*L*sin 35
To calculate the work done by a force, you need to know the magnitude of the force and the displacement of the object in the direction of the force. In this case, the person exerts a horizontal force on the block along the incline.
First, let's determine the horizontal component of the force exerted by the person. We can use the fact that the block is moving up the incline at a constant velocity, which means there is no acceleration along the incline. Therefore, the net force acting on the block in the horizontal direction must be zero. This net force is the horizontal component of the applied force minus the force due to gravity acting down the incline.
The force due to gravity can be determined using the weight of the block, which is given by:
Weight = mass * gravity
where the mass is 28 kg and gravity is approximately 9.8 m/s^2.
Weight = 28 kg * 9.8 m/s^2
Once you have the weight, you can use trigonometry to determine the force due to gravity acting down the incline and the horizontal component of the applied force.
The force due to gravity acting down the incline is given by:
Force due to gravity = Weight * sin(angle of incline)
where the angle of incline is 35 degrees.
Similarly, the horizontal component of the applied force can be determined using:
Horizontal component of applied force = Weight * cos(angle of incline)
Now that you have the horizontal component of the applied force, you can calculate the work done by multiplying it by the displacement along the incline:
Work done = Horizontal component of applied force * displacement
In this case, the displacement is given as 7 m.
So, to find the work done, follow the steps:
1. Calculate the weight of the block using the formula: Weight = mass * gravity.
2. Compute the force due to gravity acting down the incline using: Force due to gravity = Weight * sin(angle of incline).
3. Determine the horizontal component of the applied force using: Horizontal component of applied force = Weight * cos(angle of incline).
4. Multiply the horizontal component of the applied force by the displacement (7 m) to get the work done.
By following these steps, you will be able to find the work done by the person pushing the block up the frictionless incline.