Question

1a. A uniform solid ball rolls smoothly along a floor, then up a ramp inclined at 24.1 ^o. It momentarily stops when it has rolled 2.40 m along the ramp. What was its initial speed?

1b. Vector a lies in the yz plane 53.0° from the positive direction of the y-axis, has a positive z component, and has a magnitude 3.10 m. Vector b lies in the xz plane 41.0° from the positive direction of the x-axis, has a positive z component, and has a magnitude of 1.90 m. Find (a) (a times b), (b) the x-component of (axb), (c) the y-component of (axb), (d) the z-component of (axb) and (e) the angle between a and b.

Answer 1

mass S=2.4m 1Q Ⓡ = 24.1° Intial speed acceleration az-gáma v²u² = of ball=m final speed v=0 - IL m To smgroßer • Zas -4²- mgsince - 2gsmos u= 2x9.8 x 2.4x din 24.1 u=4.38ms Az Az = 3,10m Iglein 53° = 3.10 la = 3.88 mm by = lam b Sinul 53.00 ay y = 1.9 2 Tol=2.9m à - 3.88.60953 . + 3.88 din 53°2? box 9 u ។ au ojo = a be Dar à - 2.33ģ+ 3.102 6 2.9 osul n + 2.9 dinul 2 6 2.2 ^+ 1.92 26 - (2.33ý+ 3.10 2) (2.27€ +1.93') =26 = 5.89 m2 axb. 걸 = (2.33 x 1924 - - 2.2x3.28 +(0-0) 2 ax 5 = 4.43sêt 6.829 © 2-component of caxb) = 4,43 © y-comp. of cax& )=6.82 y 2.33 3.1 2,2 0 1.9 O 2-wmponent of carb) = 0 al 16) €080 = à B COSO 5,89 3.88x2.9 > O=cost(0,52) 58.67° =