What needs to be known to calculate the work done by a force acting on an object?
Correct Answer: \( \boxed{\mathrm{B}} \)
Work done is calculated using the equation:
\( W = Fd \)
where \(W\) is the work done, \(F\) is the size of the force, and \(d\) is the distance moved in the direction of the force.
Therefore, to calculate work done, it is necessary to know:
• the size of the force applied
• the distance the object moves
The time for which the force acts is not required when calculating work done.
Time is only needed when calculating power using:
\( P = \frac{W}{t} \)
Therefore, the correct row is the one that requires force and distance but not time.
Hence, the correct answer is (B).
A stone has a gravitational energy store equal to \(46\,\mathrm{J}\).
When the stone falls in air, it does \(21\,\mathrm{J}\) of work against air resistance.
What is the gain in kinetic energy stored in the stone during this fall?
Correct Answer: \( \boxed{\mathrm{B}} \)
According to the principle of conservation of energy, the loss in gravitational potential energy is equal to the gain in kinetic energy plus the energy transferred to the surroundings.
\( \Delta E_{\mathrm{p}} = \Delta E_{\mathrm{k}} + W \)
where \(W\) is the work done against air resistance.
Substituting the given values:
\( 46 = \Delta E_{\mathrm{k}} + 21 \)
\( \Delta E_{\mathrm{k}} = 46 – 21 \)
\( \Delta E_{\mathrm{k}} = 25\,\mathrm{J} \)
Therefore, \(21\,\mathrm{J}\) is dissipated due to air resistance, and the remaining \(25\,\mathrm{J}\) becomes kinetic energy of the stone.
Hence, the gain in kinetic energy is \(25\,\mathrm{J}\).
Therefore, the correct answer is (B).
A woman pushes a mower across a lawn.
Which quantities does the woman use to calculate the work she does?
Correct Answer: \( \boxed{\mathrm{B}} \)
Work done is defined as the product of the force applied and the distance moved in the direction of the force.
\( W = Fd \)
where \(W\) is the work done, \(F\) is the force applied, and \(d\) is the distance moved.
To calculate the work done while pushing the mower, the woman only needs to know the force she applies and the distance the mower moves.
Time is not required for calculating work done. Time is used when calculating power:
\( P = \frac{W}{t} \)
Therefore, the quantities needed are distance and force only.
Hence, the correct answer is (B).
