What are the forces applied on a ball in this situation?

My friend and I have an argument.

Imagine a person riding on a bike, then stretching one of his hands completely aside while holding a ball, releasing its grip completely.

basic logic tells me that if that person is fast enough the ball should stick to his hand instead of falling off, why is it? what are the forces applied to the ball in this situation?

#Mechanics

Easy Math Editor

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Comments

I assume that the plane of the person's hand is perpendicular to the direction of motion. Suppose he is going very fast. The forces look like the diagram below. The hand normal force balances the air resistance, and if the speed is just right, the friction force from the hand can balance the gravity force on the ball.

But now I'm not sure how the torques balance. The real-world situation is considerably more complicated than the picture below. It would be cool to try this in a wind tunnel.

Steven Chase - 1 year, 11 months ago

$\sum F_y = F_N - F_g$

where $F_g$ = $mg$ = $(m_{bike} + m_{person} + m_{ball})$ $g$

$\sum F_x = F_p - (F_f + F_d)$

Where:

$F_p$ is the force the biker is applying to the pedals to move the bike forward

$F_f$ is the force of friction the road applies to the tires

$F_d$ is the air resistance; it might be negligible for this problem, but in the real world this would apply.

Example: Let the following conditions be true...

$v_0$ = $10 \frac{m}{s}$

$m_{bike}$ = $15 kg$

$m_{person}$ = $60 kg$

$m_{ball}$ = $0.80 kg$

$g$ = $10 \frac{m}{s^2}$

$\mu_{friction}$ = 0.01

$F_{drag} \approx 0$

$F_{pedaling}$ = $10 N$

TO FIND: $\sum F_x$

$\sum F_x$ = $F_p - (F_f + F_d)$ ) = $10 \text{ N} - (\mu F_N + 0)$

$\mu F_N$ = $(0.01) F_g$ = $(0.01) (15 kg + 60 kg + 0.80 kg)$ $10 \frac{m}{s^2}$ = $7.58 \text{ N}$

$\sum F_x$ = $F_p - (F_f + F_d)$ = $10 \text{ N} - (7.58 \text{ N})$ = $2.42 \text{ N}$

$\sum F_x$ = $2.42 \text{ N}$

Callie Ferguson - 1 year, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$