A uniform plank of length 5.1 m and weight 235 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 458 N walk on the overhanging part of the plank before it just begins to tip?
Drawing:
0 (person)
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^ ^ (d = 1.1 from lever to edge)
We just learned torque today and this was assigned as homework...well I thought that since torque is constant....i just calculated the torque of the plank and then divided that by the mass of the person..but this is wrong..what should i do?
Huh? You need to work on the conditions of equilibrium:
1) the sum of the vertical forces is zero ( weightplank + weight man + rightsupport force + left support force) Make the support forces up, weight down. If you are wrong, you get a negative).
2) The sum of all torques about any point is zero. Choose the point on one of the forces, either support, or in the middle...it makes the equations simpler.
Now you have two equations, and three unknowns: x, and the two support forces.But the first condition lets you solve one support force in terms of the other, so you have two equations, two unknowns. Solve for x. There is a bit of algebra, so be neat.
http://physicsforums.com/archive/index.php/t-98650.html
That is a discussion of a similar problem.
Consider the torque about the support that is 1.1 m from the end. If the plank is just starting to tip, there is no force at the other support, and the net torque is zero. Let X be the distance from the right support where the person is standing. The plank weight acts through the Center of Gravity in the middle of the plank, which is 1.45 m left of the right support.
Applying a torque balance,
1.45 * 235 = 458 * X
Solve for X
thank you very much!!!
To determine the maximum distance, x, a person can walk on the overhanging part of the plank before it begins to tip, you need to consider the balance of torques.
Here's how you can approach the problem step by step:
1. Start by calculating the torque exerted by the weight of the plank itself. The weight of the plank can be calculated using the formula:
Weight = Mass × Acceleration due to gravity
Since the weight is given as 235 N, you can find the mass of the plank by dividing the weight by the acceleration due to gravity (9.8 m/s^2).
2. Next, consider the torques acting on the system. The torques that need to be balanced are the torque exerted by the weight of the plank and the torque exerted by the person.
3. The torque equation is T = F × r × sin(theta), where T is the torque, F is the force, r is the distance from the pivot point, and theta is the angle between the force and the perpendicular distance.
For the plank's torque, the force is the weight of the plank, and the distance r is the length of the plank divided by 2 (since it is symmetrically balanced on two supports).
4. For the person's torque, the force is the weight of the person (458 N), and the distance r is the distance x from the pivot point to where the person is standing.
5. Set up the equation for the balance of torques:
Torque of plank = Torque of person
Weight of plank × (length of plank / 2) = Weight of person × x
Plug in the known values and solve for x.
(Weight of plank / 2) = (Weight of person × x) / (length of plank)
Keep in mind that the length of the plank includes the overhanging part and the part supported by the left support.
6. Finally, substitute the values and solve for x. Make sure to use consistent units throughout the calculations.
Following these steps should help you determine the maximum distance, x, a person can walk on the overhanging part of the plank before it begins to tip.