Horizontal Force on a Ramp required to Accelerate a Mass

In summary, the conversation involves a 5.57 kg box on a ramp with an inclination of 38.0^\circ and a coefficient of kinetic friction of 0.28. The question is what horizontal force is needed to move the box up the ramp with an acceleration of 4.30 m/s^2. The equations used include F=ma and trigonometric functions. The solution involves calculating the force required to move the object up the ramp and the force caused by the coefficient of kinetic friction, and then adding them together to find the total horizontal force needed, which is 45.7N. However, there may be differences in signs and further clarification is needed.
  • #1
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Homework Statement



A 5.57 kg box sits on a ramp that is inclined at 38.0^\circ above the horizontal. The coefficient of kinetic friction between the box and the ramp is 0.28.

What horizontal force is required to move the box up the incline with a constant acceleration of 4.30 m/s^2?

Homework Equations



Calculation F. F=ma is important. Trig functions. Calculation of F caused by friction.

The Attempt at a Solution



I calculated the force required to move the object up the ramp using a horizontal force; m*a/cos(38), which is 23.951N.

I calculated the force caused by the μk, which is sin 52*mg, which is 12.044 N

I added these, and found the horizontal component required, which is those added/ cos 28, which gives 45.7N

I am fairly certain I'm doing this wrong though, and I would appreciate any help.

Thanks!
 
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  • #2
Welcome to PF, GiantCube.
I get the 12 and the 24 but not the 45.7. It would be nice to see your F = ma statement with the three things added to get the total force. We may have some differences in the signs.
 
  • #3
Thanks. :)

The Force is the horizontal portion of the acceleration, so (m*a*cos(38)) must the force to get over the friction, so sin(52)*m*g. Which would be F= sin(52)*m*g + (u*m*a*cos(38))

... I'm fairly certain that's wrong, but not sure why...
 

1. What is the formula for calculating the horizontal force required to accelerate a mass on a ramp?

The formula for calculating the horizontal force required to accelerate a mass on a ramp is F = mgsinθ, where F is the force, m is the mass, g is the acceleration due to gravity, and θ is the angle of the ramp.

2. How does the angle of the ramp affect the horizontal force required to accelerate a mass?

The angle of the ramp affects the horizontal force required to accelerate a mass because as the angle increases, the component of the force acting against gravity also increases. This means that a steeper ramp will require a greater horizontal force to accelerate the same mass compared to a shallower ramp.

3. What is the relationship between the mass of the object and the horizontal force required to accelerate it on a ramp?

The relationship between the mass of the object and the horizontal force required to accelerate it on a ramp is directly proportional. This means that as the mass increases, the required force also increases proportionally.

4. How does the coefficient of friction affect the horizontal force required to accelerate a mass on a ramp?

The coefficient of friction affects the horizontal force required to accelerate a mass on a ramp because it represents the resistance between the ramp and the object. A higher coefficient of friction means there is more resistance, requiring a greater horizontal force to overcome it and accelerate the object.

5. How can the horizontal force on a ramp be decreased?

The horizontal force on a ramp can be decreased by decreasing the mass of the object, decreasing the angle of the ramp, or decreasing the coefficient of friction between the object and the ramp. Alternatively, a force can be applied in the opposite direction to counteract the horizontal force and keep the object at a constant velocity.

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