What are the problem specifications of the little elf trying to stop his car from being pulled off the stand by the evil elf Lord?
The problem specifications include the mass of the elf's tiny car (120 kg), the coefficient of friction (0.23), the elf's mass (1.2 kg), the mass of the anvil (90 kg), and the force applied by the Elf Lord (25 N at an angle of 30 degrees). The goal is to determine the acceleration of the system in general terms and numerically.
Understanding the Forces at Play
The situation involves multiple forces acting on the system, including the force applied by the Elf Lord, friction, and gravity. Let's break down the forces:
1. Force applied by the Elf Lord:
The force can be broken down into horizontal and vertical components. The horizontal component (Fx) is 21.65 N, and the vertical component (Fy) is 12.5 N.
2. Force of friction:
The force of friction opposes motion and is calculated using the coefficient of friction and the normal force. It amounts to 270.48 N in this scenario.
3. Force of gravity:
The downward force of gravity on the car is 1176 N.
Calculating the Net Force:
By considering the forces in both horizontal and vertical directions, it is determined that the car will not move horizontally due to insufficient force to overcome friction. However, it will experience a downward acceleration due to gravity.
Calculating the Acceleration:
The acceleration of the system is determined by dividing the net force in the vertical direction by the total mass of the system. The resulting acceleration is -5.5 m/s^2.
In conclusion, the little elf's car will experience a downward acceleration of 5.5 m/s^2 in its attempt to resist being pulled off the stand by the evil elf Lord.