Math Problem Statement
A 74.8 kg man pushes his daughter in a stroller (combined mass of the stoller and the daughter is 19.2 kg) on a flat surface, by exerting a force of 90 N at 18degrees below the horizontal. If the coefficient of friction is 0.235, determine the net acceleration of the stoller if it moves horizontally along the level surface
Solution
We can solve this problem step by step. Here's how to calculate the net acceleration of the stroller:
Step 1: Resolve the applied force into horizontal and vertical components
The applied force () is 90 N at 18° below the horizontal:
- Horizontal component:
- Vertical component:
Step 2: Calculate the normal force
The normal force () is influenced by the vertical component of the applied force and the weight of the stroller: where and .
Step 3: Calculate the force of friction
The frictional force () is given by: where .
Step 4: Find the net horizontal force
The net horizontal force () is the horizontal applied force minus the frictional force:
Step 5: Calculate the net acceleration
The acceleration of the stroller () can be calculated using Newton's second law:
Let me calculate this for you.import math
Given data
m_stroller = 19.2 # mass of stroller in kg m_man = 74.8 # mass of man in kg (not directly needed here) F_applied = 90 # applied force in N theta = 18 # angle in degrees mu = 0.235 # coefficient of friction g = 9.8 # acceleration due to gravity in m/s^2
Step 1: Resolve applied force into components
F_x = F_applied * math.cos(math.radians(theta)) # horizontal component F_y = F_applied * math.sin(math.radians(theta)) # vertical component
Step 2: Calculate normal force
F_N = (m_stroller * g) - F_y
Step 3: Calculate frictional force
F_f = mu * F_N
Step 4: Net horizontal force
F_net = F_x - F_f
Step 5: Calculate net acceleration
a = F_net / m_stroller
a2.49547895299968532.4954789529996853successThe net acceleration of the stroller is approximately 2.50 m/s².
Do you want me to delve deeper into any specific part of the solution? Here are some related questions:
- How does the angle of the force affect the acceleration?
- What happens if the coefficient of friction changes?
- How would adding mass to the stroller influence the result?
- What if the force were applied horizontally instead of at an angle?
- How do we calculate the normal force when friction is negligible?
Tip: Always resolve forces into components when dealing with forces at an angle to simplify the calculations.
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Math Problem Analysis
Mathematical Concepts
Force resolution
Newton's second law of motion
Frictional forces
Normal force calculation
Formulas
F_x = F_applied * cos(θ)
F_y = F_applied * sin(θ)
F_N = m * g - F_y
F_f = μ * F_N
a = F_net / m
Theorems
Newton's second law of motion
Suitable Grade Level
Grades 9-12
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