A homeowner is trying to move a stubborn rock from his yard which has a mass of 1025 kg. By using a lever arm (a piece of wooden board) and a fulcrum (or pivot point) the homeowner will have a better chance of moving the rock. The homeowner places the fulcrum 24.4 cm from the rock so that it fits under the rock\'s center of weight. If the homeowner can apply a maximum force of 696.0 N, what is the minimum total length of board required to move the rock?
696*A=1025g*.244
solve for A, then length= L+.244 cm
The lever arm length from fulcrum to the end of the board is L. It must satisfy the moment-balance equation
L*696 = (1025 g)*0.244
g = 9.8 m/s^2
Solve for L. Add 0.244 m to L for the length of the board.
Thank you!!
To solve this problem, we can use the principle of torque, which is given by the equation:
Torque = Force x Lever Arm
The torque applied by the homeowner's force must be equal to the torque exerted by the rock in order for it to start moving. The torque exerted by the rock can be calculated using the following formula:
Torque (rock) = Force (rock) x Lever Arm (rock)
Since the rock is not moving initially, the torque exerted by the rock is zero, which means the torque applied by the homeowner's force must also be zero.
Now, let's break down the given information:
Mass of the rock (m) = 1025 kg
Maximum force applied by the homeowner (F) = 696.0 N
Distance of the fulcrum from the rock (Lever Arm, homeowner) = 24.4 cm = 0.244 m
To calculate the minimum total length of the board required, we need to determine the distance of the fulcrum from the rock (Lever Arm, rock) so that the torque applied by the homeowner's force is zero.
Torque (rock) = Force (rock) x Lever Arm (rock)
0 = Force (rock) x Lever Arm (rock)
We know that Force (rock) = mass of the rock x gravitational acceleration (g)
Force (rock) = m x g = (1025 kg) x (9.8 m/s^2) = 10045 N
Substituting the values into the torque equation, we get:
0 = (10045 N) x Lever Arm (rock)
Lever Arm (rock) = 0 Nm / 10045 N = 0 m
Now, we can find the minimum total length of the board:
Total Length of the board = Distance of fulcrum from the rock + Distance of fulcrum from homeowner's force
Total Length of the board = Lever Arm (rock) + Lever Arm (homeowner)
Total Length of the board = 0 m + 0.244 m = 0.244 m
Therefore, the minimum total length of the board required to move the rock is 0.244 meters.