You slide your friend with a mass of 65 kg out of the way as they are blocking the exit and keeping you from escaping from physics class where you have been tormented by problems for the last hour and a half. The coefficient of kinetic friction between the floor and your friend's shoes is 0.45 and you are able to push with 650N. How long will it take you to get your friend to their next class that is 35m down the hall from rest? (Answer: 3.5 seconds) I have worked the problem and checked my math. I get 1.99 seconds.
friction force = 65*9.81*.45 = 287 N
net force = 650-287 = 363 N
F = m a
a = 363/65 = 5.59 m/s^2
x = (1/2) a t^2
35 = .5 (5.59) t^2
t = 3.54 seconds
Thank you!
To solve this problem, we can use Newton's second law of motion and the equation for calculating the time it takes to travel a certain distance. Let's break down the steps to find the correct answer:
1. Determine the net force acting on your friend:
Since your friend was initially at rest, the net force acting on them is the force of friction opposing your push. Use the equation:
Net force = Applied force - Frictional force.
Given:
Applied force = 650N
Coefficient of kinetic friction (μ) = 0.45
Frictional force = μ * Normal force.
The normal force is equal to the weight of your friend (mg).
The acceleration of your friend is given by Newton's second law:
Net force = mass * acceleration.
Rearrange this equation to solve for the net force:
Net force = mass * acceleration = Applied force - Frictional force.
2. Find the acceleration of your friend:
Plug in the values for mass, coefficient of kinetic friction, and applied force into the rearranged equation from step 1 to solve for acceleration. The mass is given as 65 kg.
3. Use the kinematic equation to find the time:
The kinematic equation for distance traveled with constant acceleration is:
Distance = (1/2) * acceleration * time^2.
Rearrange this equation to solve for time:
Time = sqrt((2 * Distance) / acceleration).
Plug in the values for distance (35m) and acceleration (from step 2) into the rearranged equation to solve for time.
After following these steps correctly, you should find that the correct answer is 3.5 seconds, not 1.99 seconds.