A uniform ladder is 10 cm long and weights 400 N. It rests with ists upper end against a frictionless vertical wall. Its lower end rests on the ground and is prevented from slipping by a peg driven into the ground. The ladder makes a 30 degrees angle with the horizontal. The force exerted on the wall by the ladder is:

Question

A uniform ladder is 10 cm long and weights 400 N. It rests with ists upper end against a frictionless vertical wall. Its lower end rests on the ground and is prevented from slipping by a peg driven into the ground. The ladder makes a 30 degrees angle with the horizontal. The force exerted on the wall by the ladder is:

a 48N
b 74N
c 120N
d 350N
e 610N

Calculate the total horizontal forces. Remember that the sum of all forces is always zero.

I think you will have to sum moments also here, I suggest you sum moments about the ladder on the ground point. Also, you have vertical forces summing to zero also.

I think you will have to sum moments also here, I suggest you sum moments about the ladder on the ground point. Also, you have vertical forces summing to zero also.

Answer 1

To calculate the total horizontal forces, we can use the fact that the sum of all forces is always zero. Since the ladder is in equilibrium, the sum of the horizontal forces must be equal to zero.

Let's break down the forces acting on the ladder:

- Weight of the ladder: The ladder weighs 400 N and acts vertically downward.
- Normal force from the ground: The ground exerts a normal force on the ladder to balance the weight acting downward.
- Force exerted by the wall: The wall exerts a force on the ladder in the horizontal direction.

Since the ladder is in equilibrium, the sum of the vertical forces must also be equal to zero. This means that the vertical component of the weight must be balanced by the normal force from the ground.

Let's calculate the vertical component of the weight:

vertical component of weight = weight * sin(angle)
= 400 N * sin(30°)
= 200 N

Since the sum of the vertical forces is zero, the normal force from the ground must also be equal to 200 N.

To find the force exerted by the wall, we can use the fact that the sum of the horizontal forces is equal to zero.

Sum of horizontal forces = force from the wall = 0

Therefore, the force exerted on the wall by the ladder is 0 N.

Hence, the answer is 0 N.

Answer 2

To calculate the total horizontal force exerted on the wall by the ladder, we need to consider the forces acting on the ladder and apply the principle of equilibrium.

Let's analyze the forces acting on the ladder:

1. Weight of the ladder: The ladder weighs 400 N and acts vertically downward.

2. Normal force at the point where the ladder touches the ground: Since the ladder is prevented from slipping by a peg, there must be an upward normal force from the ground.

3. Force exerted on the wall: This is the horizontal force that we need to calculate.

Since the ladder is in equilibrium, the sum of all the vertical forces (weight of the ladder and normal force) must be zero. Therefore:

Vertical forces = Weight of the ladder + Normal force = 0

Weight of the ladder = - Normal force
400 N = - Normal force

Now, let's calculate the total horizontal force exerted on the wall by the ladder. We can do this by summing the forces in the horizontal direction. Since there are no other horizontal forces acting on the ladder apart from the force exerted on the wall, the total horizontal force will be equal to the force exerted on the wall:

Total horizontal force = Force exerted on the wall

To find the force exerted on the wall, we can use the concept of moments. Moments are calculated by multiplying the force by the perpendicular distance from the point of rotation.

Let's choose the point where the ladder touches the ground as the point of rotation. The perpendicular distance from this point to the line of action of the force exerted on the wall is the length of the ladder, which is 10 meters.

Using the principle of moments, we can set up the following equation:

Clockwise moments = Counterclockwise moments

Force exerted on the wall × 10 m = Weight of the ladder × perpendicular distance + Normal force × perpendicular distance

Substituting the values we know:

Force exerted on the wall × 10 m = 400 N × 10 m + (-400 N) × 10 m

Simplifying the equation:

Force exerted on the wall × 10 m = 4000 N - 4000 N

Force exerted on the wall × 10 m = 0 N

Force exerted on the wall = 0 N

So, the force exerted on the wall by the ladder is zero. Therefore, the correct answer is none of the options given.

Answer 3

D 350

Solve for Fh and plug in the other values
Fh*L*sin(theta)=w*(L/2)*cos(theta)