Final answer:
The net force acting upon the 10kg dog Fido can be calculated by resolving the four given forces into their respective components and summing up those components. The net force includes the horizontal force from the owner pulling and the friction acting in the opposite direction, as well as the vertical forces from gravity and the normal force. Fido's net force, considering the vertical forces cancel out, is 30.38N to the right.
Step-by-step explanation:
The net force acting upon Fido, a 10kg dog, can be calculated by breaking down the forces into their horizontal and vertical components and then combining them to find the total net force in each direction.
- The applied force (F_app) has a horizontal component F_appx = F_app * cos(30°) and a vertical component F_appy = F_app * sin(30°).
- The normal force (F_norm) acts directly upwards.
- The frictional force (F_frict) acts horizontally to the left.
- The force of gravity (F_grav) acts directly downwards.
First, calculate the components of the applied force:
F_appx = 67N * cos(30°) = 57.98N (to the right)
F_appy = 67N * sin(30°) = 33.5N (upwards)
Next, the net force in the horizontal direction is just the rightward component of the applied force minus the leftward frictional force:
F_netx = 57.98N (to the right) - 27.6N (to the left) = 30.38N (to the right)
And the net force in the vertical direction is the sum of the upwards forces minus the downward gravitational force:
F_nety = 33.5N (upwards) + 64.5N (upwards) - 98N (downwards) = 0N (net zero in the vertical direction)
The net force is therefore 30.38N to the right and 0N in the vertical direction, indicating no net vertical force. The dog is experiencing a net force that will cause it to accelerate to the right.