Help I'm feeling stupid. :( ("A solid sphere rolls down an incline)

[Qwurticus]

Homework Statement

"A solid sphere rolls down an incline plane without slipping. If the center of mass of the sphere has a linear acceleration of 1.21 m/s², what is the angle of the incline to the horizontal?"

Homework Equations

a = g * sin(θ)

The Attempt at a Solution

I got home from a long day at work and can't seem to make my mind click on how to solve this problem. What's throwing me off is that the linear acceleration is given in m/s², but when I googled some similar problems to this one and they all give the linear acc. in 'g'. I think I need mass but I can't figure out how to get it or if I'm even correct.

Can someone help me? Am I over-complicating this, or am I just being incredibly stupid. :( Brain doesn't want to work.

 

[Nathanael]

What's throwing me off is that the linear acceleration is given in m/s², but when I googled some similar problems to this one and they all give the linear acc. in 'g'.

"g" also has units of m/s^2 (g=9.8 m/s^2)

I think I need mass but I can't figure out how to get it or if I'm even correct.

If you think you need mass, just use "m" in place of the mass and solve.

But let me ask you, does gravitational acceleration usually depend on mass?

 

[Chestermiller]

Hi qwuarticus. Welcome to Physics Forums.

The equation you gave is correct if you can neglect the rotational inertia of the sphere. Otherwise, you need to take that into consideration. In either case, the mass of the sphere cancels out of the final result.

Chet

 

[rcgldr]

Homework Equations

a = g * sin(θ)

This would be the acceleration if there was zero friction and the sphere was sliding down the incline, but there is a friction force involved that causes the sphere to roll. You need to fix this equation to take the friction force into account.

 

[HalfLostAndSearching]

First of all, feeling "stupid" is a normal and human emotion. We all have moments where our minds don't seem to work as well as we'd like them to. It's important to take a break and come back to the problem with a fresh perspective.

In terms of solving this problem, you are on the right track. The linear acceleration is given in m/s2, which is equivalent to the acceleration due to gravity (g) on Earth. So you can use the equation a = g * sin(θ) to solve for the angle θ.

To find the mass of the sphere, you can use the formula for linear acceleration a = F/m, where F is the net force acting on the sphere and m is the mass. In this case, the only force acting on the sphere is its weight (mg), so you can rearrange the equation to solve for m.

Remember, it's important to always check your units and make sure they are consistent. In this case, the units for mass should be in kilograms (kg) and the units for acceleration should be in meters per second squared (m/s2).

I hope this helps and don't be too hard on yourself. Problem-solving can be challenging, but with practice and determination, you will be able to solve this and many more problems in the future.