Find the work W done by the 12-newton force and the 15-newton force
The Correct Answer and Explanation is :
To determine the work done by the 12-newton and 15-newton forces, we need to understand the concept of work in physics. ork is defined as the transfer of energy when a force moves an object over a distance.Mathematically, it’s expressed as:
[ W = F \times d \times \cos(\theta) ]
Where:
- ( W ) is the work done- ( F ) is the magnitude of the force- ( d ) is the displacement of the object- ( \theta ) is the angle between the force vector and the displacement vector
Assumptions: - he forces are applied in the same direction as the displacement (i.e., ( \theta = 0^\circ ), so ( \cos(0^\circ) = 1 ))- he displacement is 160 meters
Calculations:
- Work done by the 12-newton force:
[ W_{12} = 12\,\text{N} \times 160\,\text{m} \times 1 = 1,920\,\text{J} ] - Work done by the 15-newton force:
[ W_{15} = 15\,\text{N} \times 160\,\text{m} \times 1 = 2,400\,\text{J} ]
Total Work Done:
he total work done is the sum of the individual works:[ W_{\text{total}} = W_{12} + W_{15} = 1,920\,\text{J} + 2,400\,\text{J} = 4,320\,\text{J} ]
Explanation:
n this scenario, both forces are applied in the same direction as the displacement, meaning they both contribute positively to the work done on the object. The work done by each force is calculated by multiplying the force by the displacement and the cosine of the angle between them. Since the angle is zero degrees, the cosine term equals one, simplifying the calculation.
he total work done is the sum of the individual works because work is a scalar quantity and can be added algebraically. This total work results in an increase in the object’s kinetic energy, as per the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
t’s important to note that if the forces were applied at different angles to the direction of displacement, the cosine term would account for the component of each force in the direction of displacement, and the calculations would need to consider these components.
n summary, the work done by the 12-newton and 15-newton forces over a displacement of 160 meters in the same direction is 1,920 joules and 2,400 joules, respectively, leading to a total work of 4,320 joules.