Harris and Paul carry a surfboard that is 2.43 m long and weighs 143 N. Paul lifts one end with a force of 40 N.
Well, isn't it amazing how two grown individuals need a surfboard to find balance in life? But speaking of balance, let's calculate the force Harris is exerting. If Paul is lifting one end with 40 N, and the surfboard is not accelerating, that means the total force on it must be zero. And since the board weighs 143 N, Harris must be exerting a force of 103 N to balance things out. Now that's what I call teamwork!
To find out the force Harris applies to the surfboard, we need to use the principle of torque.
Torque is the measure of the turning force around an axis, and it is calculated by multiplying the force applied by the distance from the axis of rotation. In this case, the axis of rotation is the other end of the surfboard, where Harris is holding it.
Let's assume that Harris is holding the surfboard at a distance of x meters from the end where Paul is lifting it. The total torque applied to the surfboard is the sum of torques from both Harris and Paul.
The torque applied by Paul can be calculated as the force (40 N) multiplied by the length of the surfboard (2.43 m):
Torque (Paul) = 40 N * 2.43 m
Now, the total torque on the surfboard is zero since it is in equilibrium. Therefore, the torque applied by Harris can be calculated as the negative of the torque applied by Paul:
Torque (Harris) = - Torque (Paul)
Now, we can determine the force applied by Harris using the equation for torque:
Torque = Force * Distance
Therefore:
Force (Harris) * x = -Torque (Paul)
We can rearrange the equation to solve for the force applied by Harris:
Force (Harris) = -Torque (Paul) / x
Plugging in the given values:
Force (Harris) = -(40 N * 2.43 m) / x
Note that without knowing the exact value of x, we cannot determine the force Harris applies to the surfboard.
To find out the force that Harris is exerting on the other end of the surfboard, we can apply Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
Since Paul is applying a force of 40 N to lift one end of the surfboard, the surfboard exerts an equal and opposite force of 40 N on Paul. Therefore, the surfboard is experiencing a total upward force of 40 N.
Since the surfboard is in equilibrium (not accelerating), the sum of all the vertical forces acting on it should equal zero. This means that the sum of the forces exerted by Paul and Harris should be equal to the weight of the surfboard.
Given that the weight of the surfboard is 143 N, and Paul is exerting a force of 40 N, we can subtract Paul's force from the weight to determine the force exerted by Harris. Mathematically, it can be represented as:
Force exerted by Harris = Weight of surfboard - Force exerted by Paul
Force exerted by Harris = 143 N - 40 N
Force exerted by Harris = 103 N
Therefore, Harris exerts a force of 103 N on the other end of the surfboard.