To calculate the work done, we use the formula for work, which is the product of the force applied and the distance over which the force is applied in the direction of motion. The units for work are Joules (J).
Work done (\(W\)) is given by the formula:
\[ W = F \times d \]Substitute the force and distance values into the work formula:
\[ W = 50 \text{ N} \times 10 \text{ m} \]Perform the multiplication:
\[ W = 500 \text{ J} \]Therefore, the person does 500 Joules of work.
Correct Option: A) 500 JThis is the correct calculation based on the formula for work done.
The work done by a force is defined by the dot product of the force vector and the displacement vector. This can be expressed using the magnitudes of the force and displacement and the cosine of the angle between them.
Recall the formula for work done (\(W\)) by a constant force (\(F\)) causing a displacement (\(d\)):
\[ W = F \cdot d = |F| |d| \cos(\theta) \]where \(|F|\) is the magnitude of the force, \(|d|\) is the magnitude of the displacement, and \(\theta\) is the angle between the force vector and the displacement vector.
The problem states that the angle between the force and displacement vectors is 90 degrees. So, \(\theta = 90^\circ\).
Substitute this value of \(\theta\) into the work done formula:
\[ W = |F| |d| \cos(90^\circ) \]Recall the value of \(\cos(90^\circ)\). We know that \(\cos(90^\circ) = 0\).
Substitute this value back into the equation:
\[ W = |F| |d| (0) \]\[ W = 0 \]Therefore, when the angle between the force and displacement vectors is 90 degrees, the work done is zero.
Correct Option: A) Zero work
To calculate the work done, we need to use the formula that relates force, distance, and work. Work done is defined as the product of the force applied and the distance moved in the direction of the force.
The work done (\(W\)) by a constant force is given by the formula:
\[ W = F \times d \]Therefore, the work done is 50 Joules.
C) 50J — This is the correct calculation based on the formula \(W = F \times d\).
The concept of work done by a force is fundamental in physics. Work is defined as the product of the force applied and the displacement in the direction of the force. We need to analyze the formula for work done and the angle between the force and displacement vectors to determine when work is positive.
D) Force and displacement are in the same direction
When the force and displacement are in the same direction, the angle \(\theta\) between them is \(0^\circ\). Since \(\cos(0^\circ) = 1\), the work done is \(W = F \cdot d \cdot 1 = F \cdot d\), which is a positive value (assuming \(F\) and \(d\) are non-zero). This represents the maximum positive work done by the force.
The question asks about the work done when a force is applied but the object does not move. To answer this, we need to recall the definition of work in physics.
Correct Option: A) Zero work. This is correct because work requires both a force and a displacement in the direction of the force. If there is no displacement, no work is done.
The question asks to identify the quantity that is NOT necessary for work to be done in physics. We need to recall the definition of work and its mathematical formula.
Correct Option: B) Time is not necessary for work to be done. Work depends on force, distance, and the angle between them, but not on how long the force is applied or how quickly the displacement occurs.