Find the Magnitude of the Normal Force on the Slider and v'

[Northbysouth]

Homework Statement

A 2.4-lb slider is propelled upward at A along the fixed curved bar which lies in a vertical plane. If the slider is observed to have a speed of 11.3 ft/sec as it passes position B, determine (a) the magnitude N of the force exerted by the fixed rod on the slider and (b) the rate at which the speed of the slider is changing (positive if speeding up, negative if slowing down). Assume that friction is negligible.

Homework Equations

The Attempt at a Solution

For part a I drew a FBD of the slider and assigned the normal and tangential axes. I can also see that the normal force and the weight of the slider are the only forces acting on the slider.

ƩF_en = ma_n = N - mgcos(31)

m(v²/r) = N - mgcos(31)

I then solved for N and I get 6.383 lbf

I'm unsure about part b. Any suggestions?

 

[Doc Al]

ƩF_en = ma_n = N - mgcos(31)

m(v²/r) = N - mgcos(31)

What's the direction of the radial acceleration? (Check your signs.)

I'm unsure about part b. Any suggestions?

What force acts tangentially?

 

[Northbysouth]

When you say radial acceleration are you referring to the normal acceleration? I don't quite see the point you're making.

The force acting tangentially would be:

F=ma

so it would be the tangential acceleration*mass.

 

[Doc Al]

When you say radial acceleration are you referring to the normal acceleration? I don't quite see the point you're making.

You can call it the normal acceleration if you like. Which way does it point? Towards the center or away? Which way does the radial component of gravity point?

The force acting tangentially would be:

F=ma

so it would be the tangential acceleration*mass.

Well, sure. But the tangential acceleration is what you need to find. So what is the tangential force?

 

[Northbysouth]

You can call it the normal acceleration if you like. Which way does it point? Towards the center or away? Which way does the radial component of gravity point?

Oh, the positive normal axis points towards the center of the curve, so it should be:

ƩF_en = mgcos(31) - N = mv²/r

N = mgcos(31) - mv²/r

N = -2.2688 lbf

Well, sure. But the tangential acceleration is what you need to find. So what is the tangential force?

Correct me if I'm wrong:

ƩF_et = ma_t = -mgsin(31)

Solving for a_t = -gsin(31)

a_t = -32.2*sin(31)

a_t = -16.58 ft/sec²

I've just checked my answers with the system and it says they're correct.

Thanks for your help Doc Al. The second part was a lot more straight forward than I thought.