A crate of mass 9.60 kg is pulled up a rough incline with an initial speed of 1.52 m/s. The pulling force is 93.0 N parallel to the incline, which makes an angle of 21.0° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.99 m.
a) How much work is done by the gravitational force on the crate?
As I understand, work is a force over a certain distance, thus we have:
m*g*sin(theta)*d = -168.24J
Why is this negative? Because we are going upwards instead of downwards is the distance negative? Or is it because gravity is negative?
b) Determine the increase in internal energy of the crate-incline system due friction.
friction = (u_k)(N) = (u_k)(m*g*cos(theta)) = -175.31J
Again, why is this negative? Why is this cosine? I drew a picture and found that the perpendicular gravity component is mgsin(theta) which should equal N? Either I am drawing it wrong or I have misinterpreted what the "work done by gravity on the crate" is? Please someone explain, I am so confused and want to understand!
a) How much work is done by the gravitational force on the crate?
As I understand, work is a force over a certain distance, thus we have:
m*g*sin(theta)*d = -168.24J
Why is this negative? Because we are going upwards instead of downwards is the distance negative? Or is it because gravity is negative?
b) Determine the increase in internal energy of the crate-incline system due friction.
friction = (u_k)(N) = (u_k)(m*g*cos(theta)) = -175.31J
Again, why is this negative? Why is this cosine? I drew a picture and found that the perpendicular gravity component is mgsin(theta) which should equal N? Either I am drawing it wrong or I have misinterpreted what the "work done by gravity on the crate" is? Please someone explain, I am so confused and want to understand!
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Positive work is done by a force on an object, when energy is supplied to the object, tending to make it speed up. This occurs when the direction of the force is the same as the direction of the movement.
So if something falls down, the object receives energy (it speeds up and gains potential kinetic energy). This occurs when the direction of the force (weight) is the same as the direction of the movement - in this case both downwards. In this example, gravitational potential energy is the force's 'energy supply'. Gravitational potential energy has decreased and kinetic energy has increased; gravity has done work on the object.
Negative work is done by a force on an object, when energy is removed from the object, tending to make it slow down.. This occurs when the direction of the force is opposite to the direction of the movement.
In the case of lifting something up, the weight acts down but the movement is up - so negative work is done by gravity (But positive work is done by the applied force). Gravitational potential energy is increased as a result.
Friction always does negative work, as it is always in the opposite direction to the movement; this removes energy from an object, slowing it down. The energy is converted to heat.
In your calculations, if you consistently use a sign convention (e.g. up=positive, down=negative) you will get the correct signs.
I hope that's not too confusing - it should answer most of your questions.
The normal reaction is m*g*cos(theta)), not m*g*sin(theta). For an explanation, see the last part of the video in the link.
So if something falls down, the object receives energy (it speeds up and gains potential kinetic energy). This occurs when the direction of the force (weight) is the same as the direction of the movement - in this case both downwards. In this example, gravitational potential energy is the force's 'energy supply'. Gravitational potential energy has decreased and kinetic energy has increased; gravity has done work on the object.
Negative work is done by a force on an object, when energy is removed from the object, tending to make it slow down.. This occurs when the direction of the force is opposite to the direction of the movement.
In the case of lifting something up, the weight acts down but the movement is up - so negative work is done by gravity (But positive work is done by the applied force). Gravitational potential energy is increased as a result.
Friction always does negative work, as it is always in the opposite direction to the movement; this removes energy from an object, slowing it down. The energy is converted to heat.
In your calculations, if you consistently use a sign convention (e.g. up=positive, down=negative) you will get the correct signs.
I hope that's not too confusing - it should answer most of your questions.
The normal reaction is m*g*cos(theta)), not m*g*sin(theta). For an explanation, see the last part of the video in the link.