Friction on a ramp

Pull a block until it breaks free, or tilt the ramp until it slides on its own.

Friction on a ramp

Interactive

normal N196N

friction80N

acceleration0m/s²

velocity0m/s

Your pull F (up the ramp)80 NRamp angle θ0 °Mass m20 kg

Surfaces

Show the free-body diagram

The math, with your numbers

N = mg\cos\theta = 20 \times 9.8 \times \cos 0^\circ = 196\ \text{N}

f_{s,\max} = \mu_s N = 0.5 \times 196 = 98\ \text{N} \qquad f_k = \mu_k N =0.3 \times 196 = 58.8\ \text{N}

F - mg\sin\theta = 80 - 0 = 80\ \text{N} \;\Rightarrow\; |80| \le 98:\ \text{holds}

The block can stay put while tan θ ≤ μs, here up to 26.6° with no pull.

Try this

→Flat ramp, wood: raise the pull slowly from 0. Friction grows with you, then drops when the block breaks free. Where?
→With no pull, tilt the ramp until the block starts to slide. Compare the angle with tan θ = μs.
→Once it slides, lower the pull a little below the breaking point. Why does it keep going?
→Double the mass. Does the angle at which it slips change?

Want to know why it behaves like this?

The lesson “Friction, Slopes & Air Resistance” explains it step by step: Why is the first shove always the hardest?

Friction on a ramp

Pull a block until it breaks free, or tilt the ramp until it slides on its own.

Friction on a ramp

Interactive

normal N196N

friction80N

acceleration0m/s²

velocity0m/s

Your pull F (up the ramp)80 NRamp angle θ0 °Mass m20 kg

Surfaces

Show the free-body diagram

The math, with your numbers

N = mg\cos\theta = 20 \times 9.8 \times \cos 0^\circ = 196\ \text{N}

f_{s,\max} = \mu_s N = 0.5 \times 196 = 98\ \text{N} \qquad f_k = \mu_k N =0.3 \times 196 = 58.8\ \text{N}

F - mg\sin\theta = 80 - 0 = 80\ \text{N} \;\Rightarrow\; |80| \le 98:\ \text{holds}

The block can stay put while tan θ ≤ μs, here up to 26.6° with no pull.

Try this

→Flat ramp, wood: raise the pull slowly from 0. Friction grows with you, then drops when the block breaks free. Where?
→With no pull, tilt the ramp until the block starts to slide. Compare the angle with tan θ = μs.
→Once it slides, lower the pull a little below the breaking point. Why does it keep going?
→Double the mass. Does the angle at which it slips change?

Want to know why it behaves like this?

The lesson “Friction, Slopes & Air Resistance” explains it step by step: Why is the first shove always the hardest?