Two dogs pull on a toy. One pulls with a force of 10 N, the other with a force of 15 N.
(a) In what relative directions can the dogs act to give the toy the smallest acceleration?
To determine the relative directions in which the dogs can act to give the toy the smallest acceleration, we need to consider the vector addition of their forces.
The magnitude of the smallest possible acceleration occurs when the two forces are acting in the same direction. This is because when forces are parallel, their magnitudes add up to produce a larger resultant force, resulting in a larger acceleration.
Now let's analyze the forces:
- Dog 1's force has a magnitude of 10 N.
- Dog 2's force has a magnitude of 15 N.
To find the smallest acceleration, the two forces should be pointing in the same direction. Therefore, we need to calculate the vectors' sum by adding their magnitudes.
10 N + 15 N = 25 N
Since we want the smallest acceleration, the forces should act in the same direction. So, the relative directions in which the dogs can act to give the toy the smallest acceleration is for both dogs to pull in the same direction.