Question

Researchers test canine locomotion by measuring the ground reaction force (the vector sum of the normal force and the propulsion force) as dogs push down and backward with both rear legs. In one trial, a dog generated an instantaneous ground reaction force that was 1.7 times the dog's weight and angled 12 ∘ from vertical.What was the magnitude of the dog's horizontal acceleration at that moment?

Answer 1

To find the magnitude of the dog's horizontal acceleration, we can use trigonometry to find the horizontal component of the propulsion force and then apply Newton's second law.

Step-by-step explanation:

To find the magnitude of the dog's horizontal acceleration, we can first calculate the magnitude of the propulsion force using the given information. The instantaneous ground reaction force is 1.7 times the dog's weight, which means that the propulsion force is equal to 0.7 times the dog's weight. We can use trigonometry to find the horizontal component of this force:

Horizontal component of the propulsion force = Propulsion force x cos(angle)

Plugging in the values, we get: Horizontal component of the propulsion force = (0.7 x weight of the dog) x cos(12°)

Finally, we can use Newton's second law to find the magnitude of the dog's horizontal acceleration:

Horizontal acceleration = Horizontal component of the propulsion force / mass of the dog