Alex comes across a deep ravine. She was planning on this as she packed a 3.8 m portable telescoping extension ladder. It has a mass of 15 kg. She was told that in order to get to the skull’s last known location, she must get across this 2 m gap.
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| \3.8m
| \
_|_2m \____
(a) What angle will the ladder make with the horizontal? Round to the nearest whole number.
(b) Now since she has carefully lowered the ladder down to the bottom, she isn’t entirely sure if it will hold. She knows her mass is 48 kg. First we need to find the normal force due to the vertical wall. What will it be? Round to the nearest whole number. Assume the vertical wall is frictionless.
(c) Using the normal force you just found, determine the force of friction between the ladder and the horizontal surface and compare it to the maximum allowed friction force between the ladder and horizontal surface. The coefficient of static friction is 0.75. Can she make it?
(d) If you answered yes, what will happen to the friction force as she climbs down the ladder? If you answered no, would it make a difference if there was friction between the ladder and the vertical wall?
Please help, physics is my hardest subject and I'm having a lot of trouble on this question.
I can help you with this physics problem step by step.
(a) To find the angle that the ladder makes with the horizontal, we can use trigonometry. In this case, we have a right triangle formed by the ladder, the horizontal ground, and the vertical wall of the ravine. The side adjacent to the angle is the horizontal distance of 2m, while the side opposite to the angle is the height of the wall, which is 3.8m.
Let's call the angle that the ladder makes with the horizontal θ. We can use the tangent function to find this angle:
tan(θ) = opposite/adjacent
tan(θ) = 3.8/2
θ = arctan(3.8/2)
Using a calculator, we find that θ ≈ 63 degrees. Therefore, the angle that the ladder makes with the horizontal is approximately 63 degrees.
(b) To find the normal force due to the vertical wall, we need to consider the forces acting on Alex. The normal force is the force exerted by a surface perpendicular to another surface. In this case, the normal force is equal in magnitude and opposite in direction to the force exerted by Alex on the wall.
The force exerted by Alex on the wall is equal to her weight, which is given as 48 kg. The weight is calculated by multiplying the mass by the acceleration due to gravity (9.8 m/s^2):
Weight = mass * acceleration due to gravity
Weight = 48 kg * 9.8 m/s^2
Therefore, the normal force due to the vertical wall is approximately 48 kg * 9.8 m/s^2.
(c) To determine the force of friction between the ladder and the horizontal surface, we need to consider the maximum allowed friction force and compare it to the calculated force of friction. The coefficient of static friction is given as 0.75.
The force of friction (F) between two surfaces can be calculated using the equation:
F = coefficient of friction * normal force
In this case, the coefficient of static friction is 0.75, and the calculated normal force is the one found in part (b). Multiply these two values to find the force of friction.
Once you have the force of friction, compare it to the maximum allowed friction force. If the calculated force of friction is less than or equal to the maximum allowed friction force, then she can make it across.
(d) If she can make it across, the friction force as she climbs down the ladder will depend on the coefficients of friction between the ladder and the horizontal surface. In this case, we assumed a coefficient of static friction. However, if there is friction between the ladder and the vertical wall, it could influence the friction force as she climbs down.
I hope this explanation helps you understand how to approach and solve this physics problem. Let me know if you have any further questions!