How Much Force Must a Professor Exert to Control Cart Speed on a Ramp?

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SUMMARY

The discussion centers on calculating the force a professor must exert to control the speed of a cart on a 10-degree ramp. Given the cart's mass of 95 kg, an initial speed of 6 m/s, and a desired final speed of 7 m/s at the bottom of a 5-meter ramp, the correct force calculation involves determining the acceleration using the equation Vf^2 = Vi^2 + 2ax. The final force required, accounting for gravitational components and acceleration, is 285 N, confirming the professor's initial calculations after correcting a minor error.

PREREQUISITES
  • Understanding of Newton's second law (F=ma)
  • Knowledge of kinematic equations, specifically Vf^2=Vi^2 + 2ax
  • Basic trigonometry, particularly sine functions for angle calculations
  • Familiarity with gravitational force calculations (mg)
NEXT STEPS
  • Review kinematic equations in physics for motion analysis
  • Study the effects of friction on inclined planes
  • Explore advanced dynamics involving forces on inclined surfaces
  • Learn about vector components in force analysis
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone involved in mechanics or dynamics, particularly those focusing on forces and motion on inclined planes.

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Homework Statement


A professor has to haul a cart down a ramp. The ramp has an angle of about 10 degrees and is about 5 meters long. His initial speed at the top of the ramp is 6 m/s, and the cart has a mass of about 95 kg. How hard does he have to pull on the cart so that at the bottom of the ramp, its speed does not exceed 7 m/s? Neglecting friction, what is the magnitude of the minimum force he has to exert on the cart?

Initial Velocity: 6m/s
Final Velocity: 7m/s
Mass: 95kg
Distance: 5m
Angle: 10

Homework Equations



Vf^2=Vi^2 +2ax
F=ma

The Attempt at a Solution



Well first I found the acceleration of the cart.

49=36 +2a(5)
a=1.3

Then I thought that the net force would be
F=mgsin10 + ma

so

F= 95*9.8*sin(10) + 95*1.3 = 285 N

But I am still getting it wrong. Did I make a mistake someplace?
 
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Ohh nevermind I got it. I was right, dumb mistake.
 

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