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

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The discussion revolves around calculating the force a professor must exert to control the speed of a cart on a ramp. The ramp is 5 meters long with a 10-degree incline, and the cart's mass is 95 kg, starting at 6 m/s and needing to not exceed 7 m/s at the bottom. The user initially calculated the acceleration as 1.3 m/s² and the net force as 285 N, factoring in gravitational force and acceleration. After some confusion, the user confirmed their calculations were correct, attributing the earlier uncertainty to a simple mistake. The thread emphasizes the importance of careful calculation in physics problems involving forces and motion.
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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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