Question

A 25.0 kg dog decides to go for a solo hike to the top of a 850.0 m tall mountain.

How much work does the dog do?
a. 212,500 J
b. 425,000 J
c. 637,500 J
d. 850,000 J

If the dog walks along the trail and covers a distance of 2550 m, what is the average force exerted by the dog?
a. 83.33 N
b. 166.67 N
c. 250.00 N
d. 333.33 N

Imagine there is a second dog with the same mass that decides to walk the trail but takes an alternative route that zigzags back and forth (a much easier walk). Which dog does more work?
a. The first dog
b. The second dog
c. Both dogs do the same amount of work
d. Cannot be determined from the given information

Answer 1

The work done by the dog is 212,500 J. The average force exerted by the dog is approximately 333.33 N. The first dog does more work compared to the second dog.

Step-by-step explanation:

To calculate the work done by the dog, we need to multiply the force applied by the distance traveled. The work done is equal to the product of force and distance. In this case, the force is the weight of the dog, which is given by mg, where m is the mass of the dog and g is the acceleration due to gravity (9.8 m/s^2). The distance traveled is the height of the mountain, which is given as 850.0 m. Therefore, the work done by the dog is:

Work = force x distance = mg x height = 25.0 kg x 9.8 m/s^2 x 850.0 m = 212,500 J

The correct answer is (a) 212,500 J.

To find the average force exerted by the dog, we can use the formula for force:

Force = mass x acceleration

The acceleration can be found using the distance traveled and the time taken. The average velocity can be calculated as distance divided by time. Therefore, the time taken is:

Time = distance / velocity = 2550 m / 850.0 m/s = 3.0 s

The acceleration is equal to the change in velocity divided by the time taken:

Acceleration = (final velocity - initial velocity) / time = (0 - 850.0 m/s) / 3.0 s = -283.3 m/s^2

Since the dog is moving in the opposite direction of the force applied, the average force exerted by the dog is:

Average force = mass x acceleration = 25.0 kg x -283.3 m/s^2 = -7083.3 N

Taking the absolute value, the average force exerted by the dog is approximately 7083.3 N.

The correct answer is (d) 333.33 N.

Since the work done is the product of force and distance, and both dogs cover the same distance, the dog that exerts a greater force will do more work. In this case, the first dog exerts a greater force, so the first dog does more work.

The correct answer is (a) The first dog.