A uniform ladder XY of length 500cm and a mass of 20kg is placed against a smooth vertical wall with end Y uppermost and end X on a rough horizontal ground. The end Y is 400cm above the ground and the end X is 300cm out from the foot of the wall.If a girl of mass 70kg stand on a ladder at a point 300cm above the group ,what is the reaction force at the wall? and the magnitude of the reaction force at the ground and angle of this reaction force to the horizontal
Answer
A uniform ladder XY of length 500m long and mass 20kg is place against a smooth vertical wall with end Y upper most and end X on a rough horizontal ground, the end Y is 400m above ground and the end X is 300cm out from the foot of the wall. If a girl of mass 70kg stands on the ladder at a point 300cm above the ground, what is the reaction force at wall? the magnitude of the reaction force at the ground and angle of this reaction force and horizontal?
Ok pls what should I put
To find the reaction force at the wall and the magnitude and angle of the reaction force at the ground, we need to analyze the forces acting on the ladder.
Let's break down the problem step by step:
Step 1: Determine the weight of the ladder and the girl
The weight of the ladder is given as 20 kg. The weight of the girl is 70 kg. The weight of an object can be calculated using the formula: weight = mass * gravitational acceleration.
The gravitational acceleration is approximately 9.8 m/s².
Weight of ladder = 20 kg * 9.8 m/s² = 196 N
Weight of girl = 70 kg * 9.8 m/s² = 686 N
Step 2: Analyze the forces acting on the ladder
There are three forces acting on the ladder - the weight acting downward, the normal force exerted by the ground, and the reaction force exerted by the wall.
Step 3: Calculate the reaction force at the wall
Since the ladder is in equilibrium, the sum of the vertical forces must be zero. We can calculate the reaction force at the wall using this information.
Vertical forces: Weight of the ladder (acting downward) + Weight of the girl (acting downward) + Reaction force at the wall (acting upward) = 0
Reaction force at the wall = Weight of the ladder + Weight of the girl
Reaction force at the wall = 196 N + 686 N = 882 N
So, the reaction force at the wall is 882 Newtons.
Step 4: Calculate the magnitude and angle of the reaction force at the ground
To find the magnitude and angle of the reaction force at the ground, we can consider the horizontal forces acting on the ladder.
Since the ladder is in equilibrium, the sum of the horizontal forces must be zero.
Horizontal forces: Reaction force at the ground (acting to the right) = 0
This means that the magnitude of the reaction force at the ground is zero. However, there is a frictional force acting horizontally between the ladder and the ground that prevents it from slipping.
To calculate the angle of the reaction force at the ground to the horizontal, we can use trigonometry. In this case, we can use the tangent function.
Angle = arctan(height of the ladder / distance from the wall)
Angle = arctan(300 cm / 400 cm)
First, convert the measurements to meters:
Height of the ladder = 300 cm = 3 m
Distance from the wall = 400 cm = 4 m
Angle = arctan(3 m / 4 m)
Angle ≈ 36.87°
Therefore, the magnitude of the reaction force at the ground is zero, and the angle of this reaction force to the horizontal is approximately 36.87°.