2 questions, both about balancing force/torque

• achacttn
In summary: For question 2, your calculations are correct, but the answer should be positive since the wire is pulling up, so F1=639 N. In summary, the first question involves finding the horizontal component of the force applied to a gate by the bottom hinge, which is ultimately determined to be 62 N. The second question involves finding the force on the first wire holding up an object, which is determined to be approximately 639 N. These calculations are performed using the equations F=mg and torque = F x perpendicular distance.
achacttn
First question

Homework Statement

A gate is hanging on a fencepost (attached by 2 hinges).
The gate has mass 5.2kg and is 1.7m wide (weight acts down centre of gravity).
Distance between the 2 hinges is 0.7m
Find horizontal component of the force applied to the gate by the bottom hinge.

Homework Equations

F=mg,
Torque = F x perpendicular distance

The Attempt at a Solution

The top hinge exerts a force to the left and the bottom hinge to the right. Since I want to find the force that the bottom one applies, I use the top one as a pivot and try to balance the torque. However, if the gate's weight turns it clockwise, wouldn't the bottom hinge have to exert a force to the left?
I tried an alternative method where I said the overall horizontal forces must be zero, and said the horizontal forces exerted by the hinges were in equal and opposite directions. I tried finding the force exerted by the top hinge (towards the left) by making the bottom one a pivot, so that
Force of top hinge x 0.7m = 5.2kg x g x (1.7/2)
Solving for top hinge force gives 61.88N (g is taken as 9.8). So the bottom hinge must also exert a force of 61.88 but apparently this is not the answer.

Second question

Homework Statement

9.4kg object hung from ceiling using 2 wires. Each wire can hold up to 10kg.
First wire hangs at an angle of 9.08 degrees to the ceiling, and second wire hangs at an angle of 17 degrees to the ceiling. What is force on 1st wire on hanging up object?

F=mg
g = 9.8 ms^-2

The Attempt at a Solution

The total vertical force must sum to 0. So the sin of 9.08 x F1 (wire 1) + sin17 x F2 (wire 2) = 9.4 x 9.8.
Also, the horizontal forces must total to 0, so I took F1cos9.08 = F2cos17.
This gave F2 = -F1(cos9.08/cos17), and I substitute this into the F2 of the original equation. When solving for F1, the force is 639.3N, which I'm not sure is the correct answer or not because it seems very high.

question 1 answer looks good, except it should be rounded to 2 sig figs, so F= 62 N. When you take moments about the top hinge instead, the moment due to the weight still produces a cw moment, so the bot hinge force must point right to produce a counteracting ccw moment.

1. How do you calculate the net force on an object?

The net force on an object is calculated by adding up all of the individual forces acting on the object. This can be done using vector addition, where the magnitude and direction of each force is taken into account. The net force is typically measured in units of Newtons (N).

2. What is the difference between balanced and unbalanced forces?

Balanced forces are forces that are equal in magnitude and opposite in direction, resulting in a net force of zero. This means that the object will not accelerate or change its motion. Unbalanced forces, on the other hand, have a net force that is not equal to zero, causing the object to accelerate or change its motion. This is known as Newton's first law of motion.

3. How do you determine the direction of the net force?

The direction of the net force is determined by the direction of the stronger force. If two forces are acting in opposite directions, the net force will be in the direction of the stronger force. If two forces are acting in the same direction, the net force will be in that direction.

4. What is the difference between force and torque?

Force and torque are both measurements of the effect of a force on an object. Force is a straight-line push or pull, while torque is a twisting or turning force. Torque is calculated by multiplying the force by the distance from the pivot point to the point where the force is applied. Force is typically measured in Newtons (N) and torque is measured in Newton-meters (Nm).

5. How do you balance multiple torques acting on an object?

To balance multiple torques, you need to make sure that the sum of all the torques acting on the object is equal to zero. This can be done by adjusting the distance from the pivot point for each force, or by adjusting the magnitude of each force. The object will be in equilibrium when the net torque is equal to zero, meaning it is not rotating or moving.

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